SAS Output

Chapter 6 Example: Means by session for RT outcome

The MEANS Procedure

Analysis Variable : rt rt: Response Time in Milliseconds
N Obs	Mean	Std Error	Minimum	Maximum
606	1770.70	20.0709378	917.6666667	4159.14

Analysis Variable : rt rt: Response Time in Milliseconds
session: Occasion (1-6)	N Obs	Mean	Std Error	Minimum	Maximum
1	101	1961.89	54.6804707	1055.40	4159.14
2	101	1815.17	50.6541433	991.2857143	3954.37
3	101	1750.03	48.0684335	992.9259259	4086.14
4	101	1717.80	46.4101014	930.4615385	3611.80
5	101	1707.18	45.8254952	982.7666667	3290.98
6	101	1672.14	44.1344897	917.6666667	3226.00

Ch 6: 0: Saturated Means, Unstructured Variance Model

TOTAL ANSWER KEY

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structure	Unstructured
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	21
Columns in X	7
Columns in Z	0
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9155.43252939
1	1	8229.78846855	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	301985	235659	217994	202607	192154	195360
2	235659	259150	230217	213232	202092	193268
3	217994	230217	233368	205209	196919	188604
4	202607	213232	205209	217544	193676	185321
5	192154	202092	196919	193676	212098	187840
6	195360	193268	188604	185321	187840	196733

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8424	0.8212	0.7905	0.7593	0.8015
2	0.8424	1.0000	0.9361	0.8981	0.8620	0.8559
3	0.8212	0.9361	1.0000	0.9108	0.8851	0.8802
4	0.7905	0.8981	0.9108	1.0000	0.9016	0.8958
5	0.7593	0.8620	0.8851	0.9016	1.0000	0.9196
6	0.8015	0.8559	0.8802	0.8958	0.9196	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	301985	42707	7.07	<.0001
UN(2,1)	PersonID	235659	36578	6.44	<.0001
UN(2,2)	PersonID	259150	36649	7.07	<.0001
UN(3,1)	PersonID	217994	34350	6.35	<.0001
UN(3,2)	PersonID	230217	33686	6.83	<.0001
UN(3,3)	PersonID	233368	33003	7.07	<.0001
UN(4,1)	PersonID	202607	32672	6.20	<.0001
UN(4,2)	PersonID	213232	31913	6.68	<.0001
UN(4,3)	PersonID	205209	30476	6.73	<.0001
UN(4,4)	PersonID	217544	30765	7.07	<.0001
UN(5,1)	PersonID	192154	31776	6.05	<.0001
UN(5,2)	PersonID	202092	30953	6.53	<.0001
UN(5,3)	PersonID	196919	29711	6.63	<.0001
UN(5,4)	PersonID	193676	28922	6.70	<.0001
UN(5,5)	PersonID	212098	29995	7.07	<.0001
UN(6,1)	PersonID	195360	31237	6.25	<.0001
UN(6,2)	PersonID	193268	29721	6.50	<.0001
UN(6,3)	PersonID	188604	28545	6.61	<.0001
UN(6,4)	PersonID	185321	27774	6.67	<.0001
UN(6,5)	PersonID	187840	27751	6.77	<.0001
UN(6,6)	PersonID	196733	27822	7.07	<.0001

Fit Statistics
-2 Res Log Likelihood	8229.8
AIC (Smaller is Better)	8271.8
AICC (Smaller is Better)	8273.4
BIC (Smaller is Better)	8326.7

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
20	925.64	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8229.8	21	8271.8	8273.4	8294.0	8326.7	8347.7

Solution for Fixed Effects
Effect	session: Occasion (1-6)	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept		1672.14	44.1345	100	37.89	<.0001	0.05	1584.57	1759.70
session	1	289.76	32.7000	100	8.86	<.0001	0.05	224.88	354.63
session	2	143.04	26.2031	100	5.46	<.0001	0.05	91.0502	195.02
session	3	77.8986	22.8842	100	3.40	0.0010	0.05	32.4970	123.30
session	4	45.6604	20.7853	100	2.20	0.0303	0.05	4.4230	86.8979
session	5	35.0397	18.1168	100	1.93	0.0559	0.05	-0.9035	70.9829
session	6	0	.	.	.	.	.	.	.

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
session	5	100	83.60	16.72	<.0001	<.0001

Least Squares Means
Effect	session: Occasion (1-6)	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
session	1	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
session	2	1815.17	50.6541	100	35.83	<.0001	0.05	1714.68	1915.67
session	3	1750.03	48.0684	100	36.41	<.0001	0.05	1654.67	1845.40
session	4	1717.80	46.4101	100	37.01	<.0001	0.05	1625.72	1809.87
session	5	1707.18	45.8255	100	37.25	<.0001	0.05	1616.26	1798.09
session	6	1672.14	44.1345	100	37.89	<.0001	0.05	1584.57	1759.70

Differences of Least Squares Means
Effect	session: Occasion (1-6)	session: Occasion (1-6)	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
session	1	2	146.72	29.8209	100	4.92	<.0001	0.05	87.5572	205.88
session	1	3	211.86	31.3658	100	6.75	<.0001	0.05	149.63	274.09
session	1	4	244.10	33.6427	100	7.26	<.0001	0.05	177.35	310.84
session	1	5	254.72	35.8456	100	7.11	<.0001	0.05	183.60	325.83
session	1	6	289.76	32.7000	100	8.86	<.0001	0.05	224.88	354.63
session	2	3	65.1377	17.8233	100	3.65	0.0004	0.05	29.7769	100.50
session	2	4	97.3759	22.3009	100	4.37	<.0001	0.05	53.1316	141.62
session	2	5	108.00	25.7681	100	4.19	<.0001	0.05	56.8734	159.12
session	2	6	143.04	26.2031	100	5.46	<.0001	0.05	91.0502	195.02
session	3	4	32.2382	20.0232	100	1.61	0.1105	0.05	-7.4872	71.9636
session	3	5	42.8589	22.6091	100	1.90	0.0609	0.05	-1.9969	87.7147
session	3	6	77.8986	22.8842	100	3.40	0.0010	0.05	32.4970	123.30
session	4	5	10.6207	20.4625	100	0.52	0.6049	0.05	-29.9763	51.2177
session	4	6	45.6604	20.7853	100	2.20	0.0303	0.05	4.4230	86.8979
session	5	6	35.0397	18.1168	100	1.93	0.0559	0.05	-0.9035	70.9829

Ch 6: 1a: Empty Means, E-Only Variance Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structure	Variance Components
Subject Effect	PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	1
Columns in X	1
Columns in Z	0
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9228.60509392
1	1	9228.60509392	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	244123
2		244123
3			244123
4				244123
5					244123
6						244123

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
session	PersonID	244123	14036	17.39	<.0001

Fit Statistics
-2 Res Log Likelihood	9228.6
AIC (Smaller is Better)	9230.6
AICC (Smaller is Better)	9230.6
BIC (Smaller is Better)	9233.2

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
0	0.00	1.0000

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
9228.6	1	9230.6	9230.6	9231.7	9233.2	9234.2

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1770.70	20.0709	605	88.22	<.0001	0.05	1731.28	1810.12

Ch 6: 1b: Empty Means, Random Intercept Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	1
Columns in Z per Subject	1
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9228.60509392
1	1	8536.86086232	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	44900
2		44900
3			44900
4				44900
5					44900
6						44900

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	200883

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	245783	200883	200883	200883	200883	200883
2	200883	245783	200883	200883	200883	200883
3	200883	200883	245783	200883	200883	200883
4	200883	200883	200883	245783	200883	200883
5	200883	200883	200883	200883	245783	200883
6	200883	200883	200883	200883	200883	245783

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8173	0.8173	0.8173	0.8173	0.8173
2	0.8173	1.0000	0.8173	0.8173	0.8173	0.8173
3	0.8173	0.8173	1.0000	0.8173	0.8173	0.8173
4	0.8173	0.8173	0.8173	1.0000	0.8173	0.8173
5	0.8173	0.8173	0.8173	0.8173	1.0000	0.8173
6	0.8173	0.8173	0.8173	0.8173	0.8173	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
UN(1,1)	PersonID	200883	29471	6.82	<.0001
session	PersonID	44900	2825.63	15.89	<.0001

Fit Statistics
-2 Res Log Likelihood	8536.9
AIC (Smaller is Better)	8540.9
AICC (Smaller is Better)	8540.9
BIC (Smaller is Better)	8546.1

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	691.74	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8536.9	2	8540.9	8540.9	8543.0	8546.1	8548.1

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1770.70	45.4206	100	38.98	<.0001	0.05	1680.59	1860.81

Ch 6: 2a: Fixed Linear Time, Random Intercept Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	2
Columns in Z per Subject	1
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9202.30103061
1	1	8414.68804514	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	35662
2		35662
3			35662
4				35662
5					35662
6						35662

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	202422

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	238084	202422	202422	202422	202422	202422
2	202422	238084	202422	202422	202422	202422
3	202422	202422	238084	202422	202422	202422
4	202422	202422	202422	238084	202422	202422
5	202422	202422	202422	202422	238084	202422
6	202422	202422	202422	202422	202422	238084

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8502	0.8502	0.8502	0.8502	0.8502
2	0.8502	1.0000	0.8502	0.8502	0.8502	0.8502
3	0.8502	0.8502	1.0000	0.8502	0.8502	0.8502
4	0.8502	0.8502	0.8502	1.0000	0.8502	0.8502
5	0.8502	0.8502	0.8502	0.8502	1.0000	0.8502
6	0.8502	0.8502	0.8502	0.8502	0.8502	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
UN(1,1)	PersonID	202422	29470	6.87	<.0001
session	PersonID	35662	2246.48	15.87	<.0001

Fit Statistics
-2 Res Log Likelihood	8414.7
AIC (Smaller is Better)	8418.7
AICC (Smaller is Better)	8418.7
BIC (Smaller is Better)	8423.9

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	787.61	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8414.7	2	8418.7	8418.7	8420.8	8423.9	8425.9

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1899.63	46.7882	113	40.60	<.0001	0.05	1806.93	1992.33
time1	-51.5719	4.4918	504	-11.48	<.0001	0.05	-60.3968	-42.7469

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	504	131.82	131.82	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1899.63	46.7882	113	40.60	<.0001	0.05	1806.93	1992.33
Intercept at Session=2 Time=1	1848.06	45.9176	104	40.25	<.0001	0.05	1757.01	1939.11
Intercept at Session=3 Time=2	1796.49	45.4761	100	39.50	<.0001	0.05	1706.27	1886.71
Intercept at Session=4 Time=3	1744.92	45.4761	100	38.37	<.0001	0.05	1654.70	1835.13
Intercept at Session=5 Time=4	1693.34	45.9176	104	36.88	<.0001	0.05	1602.29	1784.40
Intercept at Session=6 Time=5	1641.77	46.7882	113	35.09	<.0001	0.05	1549.07	1734.47

PsuedoR2 (% Reduction) for CovEmpty vs. CovFixLin

Name	CovParm	Subject	Estimate	StdErr	ZValue	ProbZ	PseudoR2
CovEmpty	UN(1,1)	PersonID	200883	29471	6.82	<.0001	.
CovEmpty	session	PersonID	44900	2825.63	15.89	<.0001	.
CovFixLin	UN(1,1)	PersonID	202422	29470	6.87	<.0001	-0.00766
CovFixLin	session	PersonID	35662	2246.48	15.87	<.0001	0.20575

Ch 6: 2b: Random Linear Time Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	4
Columns in X	2
Columns in Z per Subject	2
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9202.30103061
1	1	8372.10246085	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	27905
2		27905
3			27905
4				27905
5					27905
6						27905

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	253258	-12701
2	time1	101	-12701	2233.83

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	1.0000	-0.5340
2	time1	101	-0.5340	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	281163	240557	227856	215155	202455	189754
2	240557	257995	219623	209156	198689	188222
3	227856	219623	239295	203157	194924	186691
4	215155	209156	203157	225063	191158	185159
5	202455	198689	194924	191158	215298	183627
6	189754	188222	186691	185159	183627	210001

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8932	0.8784	0.8553	0.8229	0.7809
2	0.8932	1.0000	0.8839	0.8680	0.8430	0.8086
3	0.8784	0.8839	1.0000	0.8754	0.8588	0.8328
4	0.8553	0.8680	0.8754	1.0000	0.8684	0.8517
5	0.8229	0.8430	0.8588	0.8684	1.0000	0.8636
6	0.7809	0.8086	0.8328	0.8517	0.8636	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	253258	37897	6.68	<.0001
UN(2,1)	PersonID	-12701	3621.98	-3.51	0.0005
UN(2,2)	PersonID	2233.83	552.92	4.04	<.0001
session	PersonID	27905	1963.42	14.21	<.0001

Fit Statistics
-2 Res Log Likelihood	8372.1
AIC (Smaller is Better)	8380.1
AICC (Smaller is Better)	8380.2
BIC (Smaller is Better)	8390.6

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
3	830.20	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8372.1	4	8380.1	8380.2	8384.3	8390.6	8394.6

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1899.63	51.4998	100	36.89	<.0001	0.05	1797.46	2001.81
time1	-51.5719	6.1567	100	-8.38	<.0001	0.05	-63.7866	-39.3571

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	100	70.17	70.17	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1899.63	51.4998	100	36.89	<.0001	0.05	1797.46	2001.81
Intercept at Session=2 Time=1	1848.06	48.5766	100	38.04	<.0001	0.05	1751.68	1944.43
Intercept at Session=3 Time=2	1796.49	46.2922	100	38.81	<.0001	0.05	1704.65	1888.33
Intercept at Session=4 Time=3	1744.92	44.7443	100	39.00	<.0001	0.05	1656.14	1833.69
Intercept at Session=5 Time=4	1693.34	44.0107	100	38.48	<.0001	0.05	1606.03	1780.66
Intercept at Session=6 Time=5	1641.77	44.1322	100	37.20	<.0001	0.05	1554.21	1729.33

Likelihood Ratio Test for FitFixLin vs. FitRandLin

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitFixLin	8414.7	2	8418.7	8423.9	.	.	.
FitRandLin	8372.1	4	8380.1	8390.6	42.5856	2	5.6579E-10

Ch 6: 3a: Fixed Quadratic, Random Linear Time Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	4
Columns in X	3
Columns in Z per Subject	2
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9193.25780414
1	1	8341.47727191	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	26176
2		26176
3			26176
4				26176
5					26176
6						26176

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	254164	-12948
2	time1	101	-12948	2332.67

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	1.0000	-0.5318
2	time1	101	-0.5318	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	280339	241216	228268	215320	202372	189424
2	241216	256776	219985	209370	198755	188140
3	228268	219985	237879	203420	195138	186855
4	215320	209370	203420	223646	191521	185571
5	202372	198755	195138	191521	214079	184286
6	189424	188140	186855	185571	184286	209178

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8991	0.8839	0.8599	0.8261	0.7822
2	0.8991	1.0000	0.8901	0.8737	0.8477	0.8118
3	0.8839	0.8901	1.0000	0.8819	0.8647	0.8377
4	0.8599	0.8737	0.8819	1.0000	0.8753	0.8580
5	0.8261	0.8477	0.8647	0.8753	1.0000	0.8709
6	0.7822	0.8118	0.8377	0.8580	0.8709	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	254164	37896	6.71	<.0001
UN(2,1)	PersonID	-12948	3620.70	-3.58	0.0003
UN(2,2)	PersonID	2332.67	551.58	4.23	<.0001
session	PersonID	26176	1844.01	14.20	<.0001

Fit Statistics
-2 Res Log Likelihood	8341.5
AIC (Smaller is Better)	8349.5
AICC (Smaller is Better)	8349.5
BIC (Smaller is Better)	8359.9

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
3	851.78	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8341.5	4	8349.5	8349.5	8353.7	8359.9	8363.9

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1945.85	52.2433	106	37.25	<.0001	0.05	1842.27	2049.43
time1	-120.90	14.5415	502	-8.31	<.0001	0.05	-149.47	-92.3303
time1*time1	13.8656	2.6348	403	5.26	<.0001	0.05	8.6860	19.0452

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	502	69.13	69.13	<.0001	<.0001
time1*time1	1	403	27.69	27.69	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1945.85	52.2433	106	37.25	<.0001	0.05	1842.27	2049.43
Intercept at Session=2 Time=1	1838.82	48.6084	100	37.83	<.0001	0.05	1742.38	1935.25
Intercept at Session=3 Time=2	1759.51	46.8223	105	37.58	<.0001	0.05	1666.67	1852.36
Intercept at Session=4 Time=3	1707.94	45.2925	105	37.71	<.0001	0.05	1618.13	1797.75
Intercept at Session=5 Time=4	1684.10	44.0458	100	38.24	<.0001	0.05	1596.72	1771.48
Intercept at Session=6 Time=5	1687.99	44.9976	108	37.51	<.0001	0.05	1598.80	1777.18
Linear Slope at Session=1 Time=0	-120.90	14.5415	502	-8.31	<.0001	0.05	-149.47	-92.3303
Linear Slope at Session=2 Time=1	-93.1687	10.0191	419	-9.30	<.0001	0.05	-112.86	-73.4747
Linear Slope at Session=3 Time=2	-65.4375	6.6968	139	-9.77	<.0001	0.05	-78.6784	-52.1965
Linear Slope at Session=4 Time=3	-37.7062	6.6968	139	-5.63	<.0001	0.05	-50.9472	-24.4653
Linear Slope at Session=5 Time=4	-9.9750	10.0191	419	-1.00	0.3200	0.05	-29.6690	9.7190
Linear Slope at Session=6 Time=5	17.7562	14.5415	502	1.22	0.2226	0.05	-10.8135	46.3259

PsuedoR2 (% Reduction) for CovRandLin vs. CovFixQuad

Name	CovParm	Subject	Estimate	StdErr	ZValue	ProbZ	PseudoR2
CovRandLin	UN(1,1)	PersonID	253258	37897	6.68	<.0001	.
CovRandLin	UN(2,2)	PersonID	2233.83	552.92	4.04	<.0001	.
CovRandLin	session	PersonID	27905	1963.42	14.21	<.0001	.
CovFixQuad	UN(1,1)	PersonID	254164	37896	6.71	<.0001	-0.003577
CovFixQuad	UN(2,2)	PersonID	2332.67	551.58	4.23	<.0001	-0.044244
CovFixQuad	session	PersonID	26176	1844.01	14.20	<.0001	0.061980

Ch 6: 3b: Random Quadratic Time Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	3
Columns in Z per Subject	3
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9193.25780414
1	1	8302.74566856	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	20298
2		20298
3			20298
4				20298
5					20298
6						20298

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	276206	-35734	3901.96
2	time1	101	-35734	25840	-3903.32
3	time1*time1	101	3901.96	-3903.32	634.47

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	1.0000	-0.4230	0.2948
2	time1	101	-0.4230	1.0000	-0.9640
3	time1*time1	101	0.2948	-0.9640	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	296504	244374	220346	204122	195702	195085
2	244374	251508	219312	208680	199315	191215
3	220346	219312	235842	209043	199808	187840
4	204122	208680	209043	225508	197182	184958
5	195702	199315	199808	197182	211735	182571
6	195085	191215	187840	184958	182571	200977

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8949	0.8333	0.7894	0.7811	0.7992
2	0.8949	1.0000	0.9005	0.8762	0.8637	0.8505
3	0.8333	0.9005	1.0000	0.9064	0.8941	0.8628
4	0.7894	0.8762	0.9064	1.0000	0.9024	0.8688
5	0.7811	0.8637	0.8941	0.9024	1.0000	0.8850
6	0.7992	0.8505	0.8628	0.8688	0.8850	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	276206	41442	6.66	<.0001
UN(2,1)	PersonID	-35734	11941	-2.99	0.0028
UN(2,2)	PersonID	25840	5864.41	4.41	<.0001
UN(3,1)	PersonID	3901.96	1949.06	2.00	0.0453
UN(3,2)	PersonID	-3903.32	982.61	-3.97	<.0001
UN(3,3)	PersonID	634.47	172.37	3.68	0.0001
session	PersonID	20298	1649.11	12.31	<.0001

Fit Statistics
-2 Res Log Likelihood	8302.7
AIC (Smaller is Better)	8316.7
AICC (Smaller is Better)	8316.9
BIC (Smaller is Better)	8335.1

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	890.51	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8302.7	7	8316.7	8316.9	8324.2	8335.1	8342.1

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1945.85	53.8497	100	36.13	<.0001	0.05	1839.01	2052.69
time1	-120.90	20.0476	100	-6.03	<.0001	0.05	-160.67	-81.1261
time1*time1	13.8656	3.4154	100	4.06	<.0001	0.05	7.0895	20.6417

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	100	36.37	36.37	<.0001	<.0001
time1*time1	1	100	16.48	16.48	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1945.85	53.8497	100	36.13	<.0001	0.05	1839.01	2052.69
Intercept at Session=2 Time=1	1838.82	48.4864	100	37.92	<.0001	0.05	1742.62	1935.01
Intercept at Session=3 Time=2	1759.51	46.9973	100	37.44	<.0001	0.05	1666.27	1852.75
Intercept at Session=4 Time=3	1707.94	45.8959	100	37.21	<.0001	0.05	1616.88	1799.00
Intercept at Session=5 Time=4	1684.10	44.2395	100	38.07	<.0001	0.05	1596.33	1771.87
Intercept at Session=6 Time=5	1687.99	44.2038	100	38.19	<.0001	0.05	1600.29	1775.69
Linear Slope at Session=1 Time=0	-120.90	20.0476	100	-6.03	<.0001	0.05	-160.67	-81.1261
Linear Slope at Session=2 Time=1	-93.1687	13.6497	100	-6.83	<.0001	0.05	-120.25	-66.0881
Linear Slope at Session=3 Time=2	-65.4375	8.0028	100	-8.18	<.0001	0.05	-81.3148	-49.5601
Linear Slope at Session=4 Time=3	-37.7062	5.9242	100	-6.36	<.0001	0.05	-49.4596	-25.9529
Linear Slope at Session=5 Time=4	-9.9750	9.9733	100	-1.00	0.3196	0.05	-29.7618	9.8118
Linear Slope at Session=6 Time=5	17.7562	16.0362	100	1.11	0.2708	0.05	-14.0591	49.5716

Likelihood Ratio Test for FitFixQuad vs. FitRandQuad

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitFixQuad	8341.5	4	8349.5	8359.9	.	.	.
FitRandQuad	8302.7	7	8316.7	8335.1	38.7316	3	1.9784E-8

Ch 6: 3b: Random Quadratic Time Model (0=Session 6)

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	3
Columns in Z per Subject	3
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9193.25780414
1	1	8302.74566856	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	20298
2		20298
3			20298
4				20298
5					20298
6						20298

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	180678	-1645.67	247.15
2	time6	101	-1645.67	11221	2441.39
3	time6*time6	101	247.15	2441.39	634.47

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	1.0000	-0.03655	0.02308
2	time6	101	-0.03655	1.0000	0.9150
3	time6*time6	101	0.02308	0.9150	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	296504	244374	220346	204122	195702	195085
2	244374	251508	219312	208680	199315	191215
3	220346	219312	235842	209043	199808	187840
4	204122	208680	209043	225508	197182	184958
5	195702	199315	199808	197182	211735	182571
6	195085	191215	187840	184958	182571	200977

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8949	0.8333	0.7894	0.7811	0.7992
2	0.8949	1.0000	0.9005	0.8762	0.8637	0.8505
3	0.8333	0.9005	1.0000	0.9064	0.8941	0.8628
4	0.7894	0.8762	0.9064	1.0000	0.9024	0.8688
5	0.7811	0.8637	0.8941	0.9024	1.0000	0.8850
6	0.7992	0.8505	0.8628	0.8688	0.8850	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	180678	27943	6.47	<.0001
UN(2,1)	PersonID	-1645.67	7298.42	-0.23	0.8216
UN(2,2)	PersonID	11221	3863.75	2.90	0.0018
UN(3,1)	PersonID	247.15	1545.72	0.16	0.8730
UN(3,2)	PersonID	2441.39	788.06	3.10	0.0019
UN(3,3)	PersonID	634.47	172.37	3.68	0.0001
session	PersonID	20298	1649.11	12.31	<.0001

Fit Statistics
-2 Res Log Likelihood	8302.7
AIC (Smaller is Better)	8316.7
AICC (Smaller is Better)	8316.9
BIC (Smaller is Better)	8335.1

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	890.51	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8302.7	7	8316.7	8316.9	8324.2	8335.1	8342.1

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1687.99	44.2038	100	38.19	<.0001	0.05	1600.29	1775.69
time6	17.7562	16.0362	100	1.11	0.2708	0.05	-14.0591	49.5716
time6*time6	13.8656	3.4154	100	4.06	<.0001	0.05	7.0895	20.6417

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time6	1	100	1.23	1.23	0.2682	0.2708
time6*time6	1	100	16.48	16.48	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=-5	1945.85	53.8497	100	36.13	<.0001	0.05	1839.01	2052.69
Intercept at Session=2 Time=-4	1838.82	48.4864	100	37.92	<.0001	0.05	1742.62	1935.01
Intercept at Session=3 Time=-3	1759.51	46.9973	100	37.44	<.0001	0.05	1666.27	1852.75
Intercept at Session=4 Time=-2	1707.94	45.8959	100	37.21	<.0001	0.05	1616.88	1799.00
Intercept at Session=5 Time=-1	1684.10	44.2395	100	38.07	<.0001	0.05	1596.33	1771.87
Intercept at Session=6 Time= 0	1687.99	44.2038	100	38.19	<.0001	0.05	1600.29	1775.69
Linear Slope at Session=1 Time=-5	-120.90	20.0476	100	-6.03	<.0001	0.05	-160.67	-81.1261
Linear Slope at Session=2 Time=-4	-93.1687	13.6497	100	-6.83	<.0001	0.05	-120.25	-66.0881
Linear Slope at Session=3 Time=-3	-65.4375	8.0028	100	-8.18	<.0001	0.05	-81.3148	-49.5601
Linear Slope at Session=4 Time=-2	-37.7062	5.9242	100	-6.36	<.0001	0.05	-49.4596	-25.9529
Linear Slope at Session=5 Time=-1	-9.9750	9.9733	100	-1.00	0.3196	0.05	-29.7618	9.8118
Linear Slope at Session=6 Time= 0	17.7562	16.0362	100	1.11	0.2708	0.05	-14.0591	49.5716

Ch 6: 4a: Fixed Slope12, Fixed Slope26, Random Intercept Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	3
Columns in Z per Subject	1
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9188.48345679
1	1	8382.68712287	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	34098
2		34098
3			34098
4				34098
5					34098
6						34098

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	202683

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	236781	202683	202683	202683	202683	202683
2	202683	236781	202683	202683	202683	202683
3	202683	202683	236781	202683	202683	202683
4	202683	202683	202683	236781	202683	202683
5	202683	202683	202683	202683	236781	202683
6	202683	202683	202683	202683	202683	236781

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8560	0.8560	0.8560	0.8560	0.8560
2	0.8560	1.0000	0.8560	0.8560	0.8560	0.8560
3	0.8560	0.8560	1.0000	0.8560	0.8560	0.8560
4	0.8560	0.8560	0.8560	1.0000	0.8560	0.8560
5	0.8560	0.8560	0.8560	0.8560	1.0000	0.8560
6	0.8560	0.8560	0.8560	0.8560	0.8560	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
UN(1,1)	PersonID	202683	29470	6.88	<.0001
session	PersonID	34098	2150.11	15.86	<.0001

Fit Statistics
-2 Res Log Likelihood	8382.7
AIC (Smaller is Better)	8386.7
AICC (Smaller is Better)	8386.7
BIC (Smaller is Better)	8391.9

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	805.80	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8382.7	2	8386.7	8386.7	8388.8	8391.9	8393.9

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	48.4187	129	40.52	<.0001	0.05	1866.09	2057.69
slope12	-163.64	23.2415	503	-7.04	<.0001	0.05	-209.31	-117.98
slope26	-32.8932	5.8104	503	-5.66	<.0001	0.05	-44.3088	-21.4776

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
slope12	1	503	49.58	49.58	<.0001	<.0001
slope26	1	503	32.05	32.05	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1961.89	48.4187	129	40.52	<.0001	0.05	1866.09	2057.69
Intercept at Session=2 Time=1	1798.25	47.0035	115	38.26	<.0001	0.05	1705.14	1891.36
Intercept at Session=3 Time=2	1765.36	45.9134	104	38.45	<.0001	0.05	1674.31	1856.40
Intercept at Session=4 Time=3	1732.46	45.5443	101	38.04	<.0001	0.05	1642.12	1822.81
Intercept at Session=5 Time=4	1699.57	45.9134	104	37.02	<.0001	0.05	1608.53	1790.61
Intercept at Session=6 Time=5	1666.68	47.0035	115	35.46	<.0001	0.05	1573.57	1759.79
Difference between slope12 and slope26	130.75	26.6265	503	4.91	<.0001	0.05	78.4380	183.06

PsuedoR2 (% Reduction) for CovEmpty vs. CovFix12Fix26

Name	CovParm	Subject	Estimate	StdErr	ZValue	ProbZ	PseudoR2
CovEmpty	UN(1,1)	PersonID	200883	29471	6.82	<.0001	.
CovEmpty	session	PersonID	44900	2825.63	15.89	<.0001	.
CovFix12Fix26	UN(1,1)	PersonID	202683	29470	6.88	<.0001	-0.00896
CovFix12Fix26	session	PersonID	34098	2150.11	15.86	<.0001	0.24058

Ch 6: 4b: Random Slope12, Fixed Slope26 Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	4
Columns in X	3
Columns in Z per Subject	2
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9188.48345679
1	1	8319.61326151	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	24168
2		24168
3			24168
4				24168
5					24168
6						24168

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	277818	-69063
2	slope12	101	-69063	59941

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	1.0000	-0.5352
2	slope12	101	-0.5352	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	301985	208755	208755	208755	208755	208755
2	208755	223800	199632	199632	199632	199632
3	208755	199632	223800	199632	199632	199632
4	208755	199632	199632	223800	199632	199632
5	208755	199632	199632	199632	223800	199632
6	208755	199632	199632	199632	199632	223800

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8030	0.8030	0.8030	0.8030	0.8030
2	0.8030	1.0000	0.8920	0.8920	0.8920	0.8920
3	0.8030	0.8920	1.0000	0.8920	0.8920	0.8920
4	0.8030	0.8920	0.8920	1.0000	0.8920	0.8920
5	0.8030	0.8920	0.8920	0.8920	1.0000	0.8920
6	0.8030	0.8920	0.8920	0.8920	0.8920	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	277818	42741	6.50	<.0001
UN(2,1)	PersonID	-69063	18932	-3.65	0.0003
UN(2,2)	PersonID	59941	12743	4.70	<.0001
session	PersonID	24168	1702.53	14.20	<.0001

Fit Statistics
-2 Res Log Likelihood	8319.6
AIC (Smaller is Better)	8327.6
AICC (Smaller is Better)	8327.7
BIC (Smaller is Better)	8338.1

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
3	868.87	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8319.6	4	8327.6	8327.7	8331.8	8338.1	8342.1

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
slope12	-163.64	31.2462	123	-5.24	<.0001	0.05	-225.50	-101.79
slope26	-32.8932	4.8916	403	-6.72	<.0001	0.05	-42.5095	-23.2768

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
slope12	1	123	27.43	27.43	<.0001	<.0001
slope26	1	403	45.22	45.22	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
Intercept at Session=2 Time=1	1798.25	46.0448	110	39.05	<.0001	0.05	1707.00	1889.50
Intercept at Session=3 Time=2	1765.36	45.2586	102	39.01	<.0001	0.05	1675.59	1855.12
Intercept at Session=4 Time=3	1732.46	44.9935	100	38.50	<.0001	0.05	1643.20	1821.73
Intercept at Session=5 Time=4	1699.57	45.2586	102	37.55	<.0001	0.05	1609.80	1789.34
Intercept at Session=6 Time=5	1666.68	46.0448	110	36.20	<.0001	0.05	1575.42	1757.93
Difference between slope12 and slope26	130.75	33.1054	153	3.95	0.0001	0.05	65.3469	196.15

Likelihood Ratio Test for FitFix12Fix26 vs. FitRand12Fix26

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitFix12Fix26	8382.7	2	8386.7	8391.9	.	.	.
FitRand12Fix26	8319.6	4	8327.6	8338.1	63.0739	2	2.0095E-14

Ch 6: 4c: Random Slope12, Random Slope26 Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	3
Columns in Z per Subject	3
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9188.48345679
1	1	8275.37431715	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	17673
2		17673
3			17673
4				17673
5					17673
6						17673

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	284312	-54270	-10644
2	slope12	101	-54270	63954	-1672.30
3	slope26	101	-10644	-1672.30	2617.28

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	1.0000	-0.4025	-0.3902
2	slope12	101	-0.4025	1.0000	-0.1293
3	slope26	101	-0.3902	-0.1293	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	301985	230042	219399	208755	198111	187467
2	230042	257400	227410	215094	202778	190462
3	219399	227410	235385	208013	198314	188615
4	208755	215094	208013	218604	193850	186768
5	198111	202778	198314	193850	207059	184921
6	187467	190462	188615	186768	184921	200747

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8251	0.8229	0.8125	0.7923	0.7614
2	0.8251	1.0000	0.9239	0.9068	0.8784	0.8379
3	0.8229	0.9239	1.0000	0.9170	0.8983	0.8677
4	0.8125	0.9068	0.9170	1.0000	0.9111	0.8916
5	0.7923	0.8784	0.8983	0.9111	1.0000	0.9070
6	0.7614	0.8379	0.8677	0.8916	0.9070	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	284312	42731	6.65	<.0001
UN(2,1)	PersonID	-54270	18230	-2.98	0.0029
UN(2,2)	PersonID	63954	13244	4.83	<.0001
UN(3,1)	PersonID	-10644	3791.26	-2.81	0.0050
UN(3,2)	PersonID	-1672.30	2097.03	-0.80	0.4252
UN(3,3)	PersonID	2617.28	636.48	4.11	<.0001
session	PersonID	17673	1435.84	12.31	<.0001

Fit Statistics
-2 Res Log Likelihood	8275.4
AIC (Smaller is Better)	8289.4
AICC (Smaller is Better)	8289.6
BIC (Smaller is Better)	8307.7

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	913.11	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8275.4	7	8289.4	8289.6	8296.8	8307.7	8314.7

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
slope12	-163.64	30.2188	100	-5.42	<.0001	0.05	-223.60	-103.69
slope26	-32.8932	6.5888	100	-4.99	<.0001	0.05	-45.9651	-19.8213

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
slope12	1	100	29.33	29.33	<.0001	<.0001
slope26	1	100	24.92	24.92	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
Intercept at Session=2 Time=1	1798.25	49.7847	100	36.12	<.0001	0.05	1699.48	1897.02
Intercept at Session=3 Time=2	1765.36	46.9899	100	37.57	<.0001	0.05	1672.13	1858.58
Intercept at Session=4 Time=3	1732.46	44.9935	100	38.50	<.0001	0.05	1643.20	1821.73
Intercept at Session=5 Time=4	1699.57	43.9044	100	38.71	<.0001	0.05	1612.46	1786.68
Intercept at Session=6 Time=5	1666.68	43.7905	100	38.06	<.0001	0.05	1579.80	1753.56
Difference between slope12 and slope26	130.75	32.5530	100	4.02	0.0001	0.05	66.1666	195.34

Likelihood Ratio Test for FitRand12Fix26 vs. FitRand12Rand26

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitRand12Fix26	8319.6	4	8327.6	8338.1	.	.	.
FitRand12Rand26	8275.4	7	8289.4	8307.7	44.2389	3	1.3427E-9

Ch 6: Random Slope12, Random Slope26 Model + Fixed Quadratic Slope26

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	4
Columns in Z per Subject	3
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9181.32379972
1	1	8268.27351110	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	17572
2		17572
3			17572
4				17572
5					17572
6						17572

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	284414	-54371	-10644
2	slope12	101	-54371	64116	-1692.57
3	slope26	101	-10644	-1692.57	2627.41

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	1.0000	-0.4026	-0.3894
2	slope12	101	-0.4026	1.0000	-0.1304
3	slope26	101	-0.3894	-0.1304	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	301985	230042	219399	208755	198111	187467
2	230042	257359	227451	215115	202778	190442
3	219399	227451	235314	208033	198324	188615
4	208755	215115	208033	218523	193870	186789
5	198111	202778	198324	193870	206988	184962
6	187467	190442	188615	186789	184962	200707

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8252	0.8230	0.8126	0.7924	0.7615
2	0.8252	1.0000	0.9243	0.9071	0.8786	0.8379
3	0.8230	0.9243	1.0000	0.9174	0.8986	0.8679
4	0.8126	0.9071	0.9174	1.0000	0.9116	0.8919
5	0.7924	0.8786	0.8986	0.9116	1.0000	0.9075
6	0.7615	0.8379	0.8679	0.8919	0.9075	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	284414	42731	6.66	<.0001
UN(2,1)	PersonID	-54371	18230	-2.98	0.0029
UN(2,2)	PersonID	64116	13243	4.84	<.0001
UN(3,1)	PersonID	-10644	3791.26	-2.81	0.0050
UN(3,2)	PersonID	-1692.57	2096.87	-0.81	0.4196
UN(3,3)	PersonID	2627.41	636.35	4.13	<.0001
session	PersonID	17572	1429.96	12.29	<.0001

Fit Statistics
-2 Res Log Likelihood	8268.3
AIC (Smaller is Better)	8282.3
AICC (Smaller is Better)	8282.5
BIC (Smaller is Better)	8300.6

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	913.05	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8268.3	7	8282.3	8282.5	8289.7	8300.6	8307.6

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
slope12	-151.96	31.0304	111	-4.90	<.0001	0.05	-213.44	-90.4680
slope26	-56.2685	15.5641	392	-3.62	0.0003	0.05	-86.8681	-25.6688
slope26*slope26	5.8438	3.5252	302	1.66	0.0984	0.05	-1.0932	12.7809

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
slope12	1	111	23.98	23.98	<.0001	<.0001
slope26	1	392	13.07	13.07	0.0003	0.0003
slope26*slope26	1	302	2.75	2.75	0.0974	0.0984

Ch 6: 5a: Fixed Time, Fixed Slope26, Random Intercept Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	3
Columns in Z per Subject	1
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9188.48345679
1	1	8382.68712287	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	34098
2		34098
3			34098
4				34098
5					34098
6						34098

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	202683

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1
1	Intercept	101	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	236781	202683	202683	202683	202683	202683
2	202683	236781	202683	202683	202683	202683
3	202683	202683	236781	202683	202683	202683
4	202683	202683	202683	236781	202683	202683
5	202683	202683	202683	202683	236781	202683
6	202683	202683	202683	202683	202683	236781

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8560	0.8560	0.8560	0.8560	0.8560
2	0.8560	1.0000	0.8560	0.8560	0.8560	0.8560
3	0.8560	0.8560	1.0000	0.8560	0.8560	0.8560
4	0.8560	0.8560	0.8560	1.0000	0.8560	0.8560
5	0.8560	0.8560	0.8560	0.8560	1.0000	0.8560
6	0.8560	0.8560	0.8560	0.8560	0.8560	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
UN(1,1)	PersonID	202683	29470	6.88	<.0001
session	PersonID	34098	2150.11	15.86	<.0001

Fit Statistics
-2 Res Log Likelihood	8382.7
AIC (Smaller is Better)	8386.7
AICC (Smaller is Better)	8386.7
BIC (Smaller is Better)	8391.9

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	805.80	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8382.7	2	8386.7	8386.7	8388.8	8391.9	8393.9

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	48.4187	129	40.52	<.0001	0.05	1866.09	2057.69
time1	-163.64	23.2415	503	-7.04	<.0001	0.05	-209.31	-117.98
slope26	130.75	26.6265	503	4.91	<.0001	0.05	78.4380	183.06

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	503	49.58	49.58	<.0001	<.0001
slope26	1	503	24.11	24.11	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1961.89	48.4187	129	40.52	<.0001	0.05	1866.09	2057.69
Intercept at Session=2 Time=1	1798.25	47.0035	115	38.26	<.0001	0.05	1705.14	1891.36
Intercept at Session=3 Time=2	1765.36	45.9134	104	38.45	<.0001	0.05	1674.31	1856.40
Intercept at Session=4 Time=3	1732.46	45.5443	101	38.04	<.0001	0.05	1642.12	1822.81
Intercept at Session=5 Time=4	1699.57	45.9134	104	37.02	<.0001	0.05	1608.53	1790.61
Intercept at Session=6 Time=5	1666.68	47.0035	115	35.46	<.0001	0.05	1573.57	1759.79
Rate of change from session 2 to 6	-32.8932	5.8104	503	-5.66	<.0001	0.05	-44.3088	-21.4776

PsuedoR2 (% Reduction) for CovEmpty vs. CovFix16Fix26

Name	CovParm	Subject	Estimate	StdErr	ZValue	ProbZ	PseudoR2
CovEmpty	UN(1,1)	PersonID	200883	29471	6.82	<.0001	.
CovEmpty	session	PersonID	44900	2825.63	15.89	<.0001	.
CovFix16Fix26	UN(1,1)	PersonID	202683	29470	6.88	<.0001	-0.00896
CovFix16Fix26	session	PersonID	34098	2150.11	15.86	<.0001	0.24058

Ch 6: 5b: Random Time, Fixed Slope26 Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	4
Columns in X	3
Columns in Z per Subject	2
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9188.48345679
1	1	8333.38121978	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	25934
2		25934
3			25934
4				25934
5					25934
6						25934

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	254290	-12982
2	time1	101	-12982	2346.46

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2
1	Intercept	101	1.0000	-0.5315
2	time1	101	-0.5315	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	280225	241308	228325	215343	202361	189378
2	241308	256606	220036	209400	198764	188128
3	228325	220036	237681	203457	195168	186878
4	215343	209400	203457	223449	191571	185628
5	202361	198764	195168	191571	213909	184378
6	189378	188128	186878	185628	184378	209063

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8999	0.8847	0.8606	0.8265	0.7824
2	0.8999	1.0000	0.8910	0.8745	0.8484	0.8122
3	0.8847	0.8910	1.0000	0.8828	0.8656	0.8383
4	0.8606	0.8745	0.8828	1.0000	0.8762	0.8588
5	0.8265	0.8484	0.8656	0.8762	1.0000	0.8719
6	0.7824	0.8122	0.8383	0.8588	0.8719	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	254290	37895	6.71	<.0001
UN(2,1)	PersonID	-12982	3620.52	-3.59	0.0003
UN(2,2)	PersonID	2346.46	551.40	4.26	<.0001
session	PersonID	25934	1827.00	14.20	<.0001

Fit Statistics
-2 Res Log Likelihood	8333.4
AIC (Smaller is Better)	8341.4
AICC (Smaller is Better)	8341.4
BIC (Smaller is Better)	8351.8

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
3	855.10	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8333.4	4	8341.4	8341.4	8345.6	8351.8	8355.8

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	52.6735	109	37.25	<.0001	0.05	1857.50	2066.29
time1	-163.64	20.8345	467	-7.85	<.0001	0.05	-204.58	-122.70
slope26	130.75	23.2213	403	5.63	<.0001	0.05	85.1007	176.40

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	467	61.69	61.69	<.0001	<.0001
slope26	1	403	31.70	31.70	<.0001	<.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1961.89	52.6735	109	37.25	<.0001	0.05	1857.50	2066.29
Intercept at Session=2 Time=1	1798.25	49.3756	107	36.42	<.0001	0.05	1700.37	1896.13
Intercept at Session=3 Time=2	1765.36	46.6212	103	37.87	<.0001	0.05	1672.89	1857.82
Intercept at Session=4 Time=3	1732.46	44.7989	100	38.67	<.0001	0.05	1643.59	1821.34
Intercept at Session=5 Time=4	1699.57	44.0246	100	38.60	<.0001	0.05	1612.23	1786.91
Intercept at Session=6 Time=5	1666.68	44.3533	102	37.58	<.0001	0.05	1578.70	1754.65
Rate of change from session 2 to 6	-32.8932	6.9936	163	-4.70	<.0001	0.05	-46.7028	-19.0836

Likelihood Ratio Test for FitFix16Fix26 vs. FitRand16Fix26

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitFix16Fix26	8382.7	2	8386.7	8391.9	.	.	.
FitRand16Fix26	8333.4	4	8341.4	8351.8	49.3059	2	1.965E-11

Ch 6: 5c: Random Time, Random Slope26 Model

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	REML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	3
Columns in Z per Subject	3
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Res Log Like	Criterion
0	1	9188.48345679
1	1	8275.37431715	0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	17673
2		17673
3			17673
4				17673
5					17673
6						17673

Estimated R Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000
2		1.0000
3			1.0000
4				1.0000
5					1.0000
6						1.0000

Estimated G Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	284312	-54270	43626
2	time1	101	-54270	63954	-65626
3	slope26	101	43626	-65626	69916

Estimated G Correlation Matrix
Row	Effect	PersonID: Participant ID	Col1	Col2	Col3
1	Intercept	101	1.0000	-0.4025	0.3094
2	time1	101	-0.4025	1.0000	-0.9814
3	slope26	101	0.3094	-0.9814	1.0000

Estimated V Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	301985	230042	219399	208755	198111	187467
2	230042	257400	227410	215094	202778	190462
3	219399	227410	235385	208013	198314	188615
4	208755	215094	208013	218604	193850	186768
5	198111	202778	198314	193850	207059	184921
6	187467	190462	188615	186768	184921	200747

Estimated V Correlation Matrix for PersonID 101
Row	Col1	Col2	Col3	Col4	Col5	Col6
1	1.0000	0.8251	0.8229	0.8125	0.7923	0.7614
2	0.8251	1.0000	0.9239	0.9068	0.8784	0.8379
3	0.8229	0.9239	1.0000	0.9170	0.8983	0.8677
4	0.8125	0.9068	0.9170	1.0000	0.9111	0.8916
5	0.7923	0.8784	0.8983	0.9111	1.0000	0.9070
6	0.7614	0.8379	0.8677	0.8916	0.9070	1.0000

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	284312	42731	6.65	<.0001
UN(2,1)	PersonID	-54270	18230	-2.98	0.0029
UN(2,2)	PersonID	63954	13244	4.83	<.0001
UN(3,1)	PersonID	43626	19049	2.29	0.0220
UN(3,2)	PersonID	-65626	14154	-4.64	<.0001
UN(3,3)	PersonID	69916	15434	4.53	<.0001
session	PersonID	17673	1435.84	12.31	<.0001

Fit Statistics
-2 Res Log Likelihood	8275.4
AIC (Smaller is Better)	8289.4
AICC (Smaller is Better)	8289.6
BIC (Smaller is Better)	8307.7

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	913.11	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8275.4	7	8289.4	8289.6	8296.8	8307.7	8314.7

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
time1	-163.64	30.2188	100	-5.42	<.0001	0.05	-223.60	-103.69
slope26	130.75	32.5530	100	4.02	0.0001	0.05	66.1666	195.34

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	100	29.33	29.33	<.0001	<.0001
slope26	1	100	16.13	16.13	<.0001	0.0001

Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept at Session=1 Time=0	1961.89	54.6805	100	35.88	<.0001	0.05	1853.41	2070.38
Intercept at Session=2 Time=1	1798.25	49.7847	100	36.12	<.0001	0.05	1699.48	1897.02
Intercept at Session=3 Time=2	1765.36	46.9899	100	37.57	<.0001	0.05	1672.13	1858.58
Intercept at Session=4 Time=3	1732.46	44.9935	100	38.50	<.0001	0.05	1643.20	1821.73
Intercept at Session=5 Time=4	1699.57	43.9044	100	38.71	<.0001	0.05	1612.46	1786.68
Intercept at Session=6 Time=5	1666.68	43.7905	100	38.06	<.0001	0.05	1579.80	1753.56
Rate of change from session 2 to 6	-32.8932	6.5888	100	-4.99	<.0001	0.05	-45.9651	-19.8213

Likelihood Ratio Test for FitRand16Fix26 vs. FitRand16Rand26

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitRand16Fix26	8333.4	4	8341.4	8351.8	.	.	.
FitRand16Rand26	8275.4	7	8289.4	8307.7	58.0069	3	1.5665E-12

Ch 6: 6a Fixed Asymptote Fixed Amount Fixed Rate Model

The NLMIXED Procedure

Specifications
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Distribution for Dependent Variable	Normal
Optimization Technique	Newton-Raphson
Integration Method	None

Dimensions
Observations Used	606
Observations Not Used	0
Total Observations	606
Parameters	4

Parameters
fasymp	famount	frate	SDE	NegLogLike
1600	300	-1	600	4638.14263

Iteration History
Iter		Calls	NegLogLike	Diff	MaxGrad	Slope
1	*	19	4631.13397	7.008659	0.635601	-1452257
2	*	27	4631.1316	0.002371	0.398972	-0.00545
3	*	35	4631.1279	0.003703	0.349025	-0.00405
4	*	47	4625.36584	5.762055	11.20618	-0.06333
5	*	55	4624.07701	1.288829	1.988075	-1.51207
6	*	65	4609.76706	14.30995	13.15668	-3.73214
7	*	74	4609.06404	0.703022	6.328134	-7.5442
8	*	82	4608.15817	0.905866	3.859538	-2.62856
9	*	90	4607.16602	0.992149	0.234699	-1.46072
10	*	98	4606.91802	0.248002	0.261371	-0.34784
11	*	106	4606.77229	0.145727	0.95211	-0.19106
12		115	4606.69093	0.081359	1.228705	-0.61641
13		123	4606.60991	0.081021	1.385862	-0.21847
14		131	4606.58001	0.029905	0.313145	-0.05105
15		139	4606.57696	0.003047	0.0445	-0.0057
16		147	4606.57692	0.000044	0.000599	-0.00009
17		155	4606.57692	1.102E-8	2.256E-7	-2.2E-8

NOTE: ABSGCONV convergence criterion satisfied.

Fit Statistics
-2 Log Likelihood	9213.2
AIC (smaller is better)	9221.2
AICC (smaller is better)	9221.2
BIC (smaller is better)	9238.8

Parameter Estimates
Parameter	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper	Gradient
fasymp	1675.25	54.8302	606	30.55	<.0001	0.05	1567.57	1782.93	1.214E-9
famount	284.71	64.5956	606	4.41	<.0001	0.05	157.85	411.57	3.83E-10
frate	-0.6698	0.4247	606	-1.58	0.1153	0.05	-1.5039	0.1643	2.256E-7
SDE	484.28	13.9108	606	34.81	<.0001	0.05	456.97	511.60	7.67E-11

Additional Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Fixed Asymptote	1675.25	54.8302	606	30.55	<.0001	0.05	1567.57	1782.93
Fixed Amount	284.71	64.5956	606	4.41	<.0001	0.05	157.85	411.57
Fixed Rate	-0.6698	0.4247	606	-1.58	0.1153	0.05	-1.5039	0.1643
Level-1 Residual E Variance	234532	13474	606	17.41	<.0001	0.05	208071	260993
Fixed Intercept	1959.96	47.8092	606	41.00	<.0001	0.05	1866.07	2053.85
Session=1 Time=0 Predicted Mean	1959.96	47.8092	606	41.00	<.0001	0.05	1866.07	2053.85
Session=2 Time=1 Predicted Mean	1820.97	36.2921	606	50.18	<.0001	0.05	1749.69	1892.24
Session=3 Time=2 Predicted Mean	1749.83	30.7804	606	56.85	<.0001	0.05	1689.38	1810.28
Session=4 Time=3 Predicted Mean	1713.42	23.4668	606	73.01	<.0001	0.05	1667.33	1759.51
Session=5 Time=4 Predicted Mean	1694.79	27.9046	606	60.74	<.0001	0.05	1639.98	1749.59
Session=6 Time=5 Predicted Mean	1685.25	36.3818	606	46.32	<.0001	0.05	1613.80	1756.70

Ch 6: 6b Random Asymptote Fixed Amount Fixed Rate Model

The NLMIXED Procedure

Specifications
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Distribution for Dependent Variable	Normal
Random Effects	U0i
Distribution for Random Effects	Normal
Subject Variable	PersonID
Optimization Technique	Newton-Raphson
Integration Method	Adaptive Gaussian Quadrature

Dimensions
Observations Used	606
Observations Not Used	0
Total Observations	606
Subjects	101
Max Obs per Subject	6
Parameters	5
Quadrature Points	1

Parameters
fasymp	famount	frate	sdE	sdU0	NegLogLike
1675	284	-0.7	474	10	4606.26946

Iteration History
Iter		Calls	NegLogLike	Diff	MaxGrad	Slope
1	*	22	4284.53968	321.7298	2.367127	-111.104
2	*	32	4260.22159	24.31809	0.670709	-67.5039
3	*	50	4206.38334	53.83825	3.326456	-8.69512
4		59	4203.3169	3.06644	0.288049	-10.2723
5		68	4202.06922	1.247678	0.032395	-2.22741
6		77	4202.01577	0.053447	0.001225	-0.10335
7		86	4202.01562	0.00015	2.984E-6	-0.0003

NOTE: ABSGCONV convergence criterion satisfied.

Fit Statistics
-2 Log Likelihood	8404.0
AIC (smaller is better)	8414.0
AICC (smaller is better)	8414.1
BIC (smaller is better)	8427.1

Parameter Estimates
Parameter	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper	Gradient
fasymp	1675.25	49.2032	100	34.05	<.0001	0.05	1577.63	1772.87	3.596E-8
famount	284.71	24.5497	100	11.60	<.0001	0.05	236.00	333.41	1.111E-8
frate	-0.6698	0.1614	100	-4.15	<.0001	0.05	-0.9900	-0.3495	2.984E-6
sdE	184.05	5.7914	100	31.78	<.0001	0.05	172.56	195.54	-1.54E-7
sdU0	447.95	32.4067	100	13.82	<.0001	0.05	383.65	512.24	-1.58E-6

Additional Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Fixed Asymptote	1675.25	49.2032	100	34.05	<.0001	0.05	1577.63	1772.87
Fixed Intercept	1959.96	48.1335	100	40.72	<.0001	0.05	1864.46	2055.45
Fixed Amount	284.71	24.5497	100	11.60	<.0001	0.05	236.00	333.41
Fixed Rate	-0.6698	0.1614	100	-4.15	<.0001	0.05	-0.9900	-0.3495
Level-1 Residual E Variance	33875	2131.80	100	15.89	<.0001	0.05	29645	38104
Level-2 Random Asymptote U0 Variance	200656	29033	100	6.91	<.0001	0.05	143055	258256
Fixed Intercept	1959.96	48.1335	100	40.72	<.0001	0.05	1864.46	2055.45
Session=1 Time=0 Predicted Mean	1959.96	48.1335	100	40.72	<.0001	0.05	1864.46	2055.45
Session=2 Time=1 Predicted Mean	1820.97	46.6577	100	39.03	<.0001	0.05	1728.40	1913.53
Session=3 Time=2 Predicted Mean	1749.83	46.0819	100	37.97	<.0001	0.05	1658.40	1841.25
Session=4 Time=3 Predicted Mean	1713.42	45.4558	100	37.69	<.0001	0.05	1623.24	1803.60
Session=5 Time=4 Predicted Mean	1694.79	45.8166	100	36.99	<.0001	0.05	1603.89	1785.68
Session=6 Time=5 Predicted Mean	1685.25	46.6678	100	36.11	<.0001	0.05	1592.66	1777.84

Ch 6: 6c Random Asymptote Random Amount Fixed Rate Model

The NLMIXED Procedure

Specifications
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Distribution for Dependent Variable	Normal
Random Effects	U0i U1i
Distribution for Random Effects	Normal
Subject Variable	PersonID
Optimization Technique	Newton-Raphson
Integration Method	Adaptive Gaussian Quadrature

Dimensions
Observations Used	606
Observations Not Used	0
Total Observations	606
Subjects	101
Max Obs per Subject	6
Parameters	7
Quadrature Points	1

Parameters
fasymp	famount	frate	sdE	sdU0	sdU01	sdU1	NegLogLike
1675	284	-0.7	184	447	1	10	4201.89546

Iteration History
Iter		Calls	NegLogLike	Diff	MaxGrad	Slope
1	*	24	4174.64461	27.25085	2.966575	-3.60103
2	*	35	4167.35546	7.28915	0.533266	-27.9792
3	*	46	4163.88965	3.465811	0.105741	-6.22568
4	*	57	4163.76983	0.119817	0.009234	-0.23309
5	*	68	4163.76888	0.000952	0.000415	-0.00107
6	*	88	4163.70036	0.068523	0.231942	-0.00046
7	*	99	4163.67024	0.030114	0.005638	-0.05814
8	*	110	4163.67021	0.000031	5.753E-6	-0.00006

NOTE: ABSGCONV convergence criterion satisfied.

Fit Statistics
-2 Log Likelihood	8327.3
AIC (smaller is better)	8341.3
AICC (smaller is better)	8341.5
BIC (smaller is better)	8359.6

Parameter Estimates
Parameter	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper	Gradient
fasymp	1683.48	45.4523	99	37.04	<.0001	0.05	1593.30	1773.67	-3.75E-6
famount	279.94	33.5457	99	8.35	<.0001	0.05	213.38	346.51	-1.6E-7
frate	-0.7533	0.1181	99	-6.38	<.0001	0.05	-0.9877	-0.5189	5.753E-6
sdE	151.79	5.3423	99	28.41	<.0001	0.05	141.19	162.39	-2.93E-7
sdU0	436.83	31.8999	99	13.69	<.0001	0.05	373.54	500.13	-6.16E-7
sdU01	81.5159	90.6700	99	0.90	0.3708	0.05	-98.3930	261.42	-3.36E-6
sdU1	277.95	28.4728	99	9.76	<.0001	0.05	221.45	334.44	-1.88E-7

Additional Estimates
Label	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Fixed Asymptote	1683.48	45.4523	99	37.04	<.0001	0.05	1593.30	1773.67
Fixed Amount	279.94	33.5457	99	8.35	<.0001	0.05	213.38	346.51
Fixed Rate	-0.7533	0.1181	99	-6.38	<.0001	0.05	-0.9877	-0.5189
Level-1 Residual E Variance	23039	1621.76	99	14.21	<.0001	0.05	19821	26257
Level-2 Random Asymptote U0 Variance	190823	27870	99	6.85	<.0001	0.05	135523	246122
Level-2 Asymptote-Amount U01 Covariance	6644.84	14782	99	0.45	0.6540	0.05	-22686	35976
Level-2 Random Amount U1 Variance	77254	15828	99	4.88	<.0001	0.05	45848	108660
Level-2 Asymptote-Amount Correlation	0.05473	0.1224	99	0.45	0.6557	0.05	-0.1881	0.2975
Fixed Intercept	1963.43	54.7439	99	35.87	<.0001	0.05	1854.80	2072.05
Session=1 Time=0 Predicted Mean	1963.43	54.7439	99	35.87	<.0001	0.05	1854.80	2072.05
Session=2 Time=1 Predicted Mean	1815.29	47.2407	99	38.43	<.0001	0.05	1721.55	1909.03
Session=3 Time=2 Predicted Mean	1745.54	45.0393	99	38.76	<.0001	0.05	1656.17	1834.91
Session=4 Time=3 Predicted Mean	1712.70	44.3143	99	38.65	<.0001	0.05	1624.77	1800.63
Session=5 Time=4 Predicted Mean	1697.24	44.3919	99	38.23	<.0001	0.05	1609.16	1785.32
Session=6 Time=5 Predicted Mean	1689.96	44.7051	99	37.80	<.0001	0.05	1601.26	1778.67

Ch 6: 6d Random Asymptote Random Amount Random Rate Model

The NLMIXED Procedure

Specifications
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Distribution for Dependent Variable	Normal
Random Effects	U0i U1i U2i
Distribution for Random Effects	Normal
Subject Variable	PersonID
Optimization Technique	Newton-Raphson
Integration Method	Adaptive Gaussian Quadrature

Ch 6: 0: Saturated Means, Unstructured Variance Model

Using ML Instead of REML

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structure	Unstructured
Subject Effect	PersonID
Estimation Method	ML
Residual Variance Method	None
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	21
Columns in X	7
Columns in Z	0
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Log Like	Criterion
0	1	9212.98932385
1	1	8278.08882241	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	298995	42074	7.11	<.0001
UN(2,1)	PersonID	233326	36036	6.47	<.0001
UN(2,2)	PersonID	256584	36106	7.11	<.0001
UN(3,1)	PersonID	215836	33842	6.38	<.0001
UN(3,2)	PersonID	227937	33187	6.87	<.0001
UN(3,3)	PersonID	231057	32514	7.11	<.0001
UN(4,1)	PersonID	200601	32188	6.23	<.0001
UN(4,2)	PersonID	211120	31440	6.71	<.0001
UN(4,3)	PersonID	203177	30024	6.77	<.0001
UN(4,4)	PersonID	215390	30310	7.11	<.0001
UN(5,1)	PersonID	190251	31306	6.08	<.0001
UN(5,2)	PersonID	200091	30494	6.56	<.0001
UN(5,3)	PersonID	194969	29271	6.66	<.0001
UN(5,4)	PersonID	191758	28494	6.73	<.0001
UN(5,5)	PersonID	209998	29551	7.11	<.0001
UN(6,1)	PersonID	193426	30774	6.29	<.0001
UN(6,2)	PersonID	191355	29281	6.54	<.0001
UN(6,3)	PersonID	186737	28122	6.64	<.0001
UN(6,4)	PersonID	183486	27363	6.71	<.0001
UN(6,5)	PersonID	185981	27340	6.80	<.0001
UN(6,6)	PersonID	194785	27410	7.11	<.0001

Fit Statistics
-2 Log Likelihood	8278.1
AIC (Smaller is Better)	8332.1
AICC (Smaller is Better)	8334.7
BIC (Smaller is Better)	8402.7

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
20	934.90	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8278.1	27	8332.1	8334.7	8360.7	8402.7	8429.7

Solution for Fixed Effects
Effect	session: Occasion (1-6)	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept		1672.14	43.9155	101	38.08	<.0001	0.05	1585.02	1759.25
session	1	289.76	32.5377	101	8.91	<.0001	0.05	225.21	354.30
session	2	143.04	26.0730	101	5.49	<.0001	0.05	91.3145	194.76
session	3	77.8986	22.7706	101	3.42	0.0009	0.05	32.7278	123.07
session	4	45.6604	20.6822	101	2.21	0.0295	0.05	4.6326	86.6883
session	5	35.0397	18.0269	101	1.94	0.0547	0.05	-0.7208	70.8002
session	6	0	.	.	.	.	.	.	.

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
session	5	101	84.44	16.89	<.0001	<.0001

Ch 6: 1b: Empty Means, Random Intercept Model

Using ML Instead of REML

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	ML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	2
Columns in X	1
Columns in Z per Subject	1
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Log Like	Criterion
0	1	9236.44069077
1	1	8546.32568749	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
UN(1,1)	PersonID	198820	29035	6.85	<.0001
session	PersonID	44900	2825.63	15.89	<.0001

Fit Statistics
-2 Log Likelihood	8546.3
AIC (Smaller is Better)	8552.3
AICC (Smaller is Better)	8552.4
BIC (Smaller is Better)	8560.2

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
1	690.12	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8546.3	3	8552.3	8552.4	8555.5	8560.2	8563.2

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1770.70	45.1952	101	39.18	<.0001	0.05	1681.05	1860.36

Likelihood Ratio Test for FitMLEmptyRI vs. FitMLSatUN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitMLEmptyRI	8546.3	3	8552.3	8560.2	.	.	.
FitMLSatUN	8278.1	27	8332.1	8402.7	268.237	24	0

Ch 6: 3b: Random Quadratic Time Model

Using ML instead of REML

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	ML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	3
Columns in Z per Subject	3
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Log Like	Criterion
0	1	9213.75870052
1	1	8321.76659796	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	273306	40828	6.69	<.0001
UN(2,1)	PersonID	-35262	11765	-3.00	0.0027
UN(2,2)	PersonID	25438	5781.19	4.40	<.0001
UN(3,1)	PersonID	3845.38	1920.35	2.00	0.0452
UN(3,2)	PersonID	-3837.76	968.79	-3.96	<.0001
UN(3,3)	PersonID	622.81	169.99	3.66	0.0001
session	PersonID	20298	1649.11	12.31	<.0001

Fit Statistics
-2 Log Likelihood	8321.8
AIC (Smaller is Better)	8341.8
AICC (Smaller is Better)	8342.1
BIC (Smaller is Better)	8367.9

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	891.99	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8321.8	10	8341.8	8342.1	8352.4	8367.9	8377.9

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1945.85	53.5825	101	36.32	<.0001	0.05	1839.56	2052.14
time1	-120.90	19.9481	101	-6.06	<.0001	0.05	-160.47	-81.3283
time1*time1	13.8656	3.3985	101	4.08	<.0001	0.05	7.1240	20.6073

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
time1	1	101	36.73	36.73	<.0001	<.0001
time1*time1	1	101	16.65	16.65	<.0001	<.0001

Likelihood Ratio Test for FitMLEmptyRI vs. FitMLRandQuad

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitMLEmptyRI	8546.3	3	8552.3	8560.2	.	.	.
FitMLRandQuad	8321.8	10	8341.8	8367.9	224.559	7	0

Likelihood Ratio Test for FitMLRandQuad vs. FitMLSatUN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitMLRandQuad	8321.8	10	8341.8	8367.9	.	.	.
FitMLSatUN	8278.1	27	8332.1	8402.7	43.6778	17	.000382028

Ch 6: 4c: Random Slope12, Random Slope26 Model

Using ML instead of REML

The Mixed Procedure

Model Information
Data Set	WORK.CHAPTER6
Dependent Variable	rt
Covariance Structures	Unstructured, Variance Components
Subject Effects	PersonID, PersonID
Estimation Method	ML
Residual Variance Method	Parameter
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Satterthwaite

Dimensions
Covariance Parameters	7
Columns in X	3
Columns in Z per Subject	3
Subjects	101
Max Obs per Subject	6

Number of Observations
Number of Observations Read	606
Number of Observations Used	606
Number of Observations Not Used	0

Iteration History
Iteration	Evaluations	-2 Log Like	Criterion
0	1	9213.34412474
1	1	8298.94660558	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr Z
UN(1,1)	PersonID	281322	42099	6.68	<.0001
UN(2,1)	PersonID	-53558	17962	-2.98	0.0029
UN(2,2)	PersonID	63041	13054	4.83	<.0001
UN(3,1)	PersonID	-10538	3735.10	-2.82	0.0048
UN(3,2)	PersonID	-1620.74	2066.55	-0.78	0.4329
UN(3,3)	PersonID	2573.86	627.53	4.10	<.0001
session	PersonID	17673	1435.84	12.31	<.0001

Fit Statistics
-2 Log Likelihood	8298.9
AIC (Smaller is Better)	8318.9
AICC (Smaller is Better)	8319.3
BIC (Smaller is Better)	8345.1

Null Model Likelihood Ratio Test
DF	Chi-Square	Pr > ChiSq
6	914.40	<.0001

Information Criteria
Neg2LogLike	Parms	AIC	AICC	HQIC	BIC	CAIC
8298.9	10	8318.9	8319.3	8329.5	8345.1	8355.1

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > \|t\|	Alpha	Lower	Upper
Intercept	1961.89	54.4091	101	36.06	<.0001	0.05	1853.96	2069.83
slope12	-163.64	30.0689	101	-5.44	<.0001	0.05	-223.29	-104.00
slope26	-32.8932	6.5561	101	-5.02	<.0001	0.05	-45.8986	-19.8877

Type 3 Tests of Fixed Effects
Effect	Num DF	Den DF	Chi-Square	F Value	Pr > ChiSq	Pr > F
slope12	1	101	29.62	29.62	<.0001	<.0001
slope26	1	101	25.17	25.17	<.0001	<.0001

Likelihood Ratio Test for FitMLEmptyRI vs. FitMLRand12Rand26

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitMLEmptyRI	8546.3	3	8552.3	8560.2	.	.	.
FitMLRand12Rand26	8298.9	10	8318.9	8345.1	247.379	7	0

Likelihood Ratio Test for FitMLRand12Rand26 vs. FitMLSatUN

Name	Neg2LogLike	Parms	AIC	BIC	DevDiff	DFdiff	Pvalue
FitMLRand12Rand26	8298.9	10	8318.9	8345.1	.	.	.
FitMLSatUN	8278.1	27	8332.1	8402.7	20.8578	17	0.23272