------------------------------------------------------------------------------------------------------------------------------------------------------
name: STATA_Chapter7a
log: C:\Dropbox\PilesOfVariance\Chapter7a\STATA\STATA_Chapter7a_Output.smcl
log type: smcl
opened on: 12 Jan 2015, 10:30:51
.
. display as result "Chapter 7a: Descriptive Statistics for Time-Invariant Variables"
Chapter 7a: Descriptive Statistics for Time-Invariant Variables
. preserve
. collapse women baseage, by(personid)
. summarize women baseage
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
women | 105 .7333333 .4443376 0 1
baseage | 105 80.12967 6.105009 69.70294 95.30732
. restore
.
. display as result "Chapter 7a: Descriptive Statistics for Time-Varying Variables"
Chapter 7a: Descriptive Statistics for Time-Varying Variables
. summarize symptoms
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
symptoms | 509 1.273084 1.324394 0 5
.
. display as result "Eq 7a.3: Empty Means, Random Intercept Model"
Eq 7a.3: Empty Means, Random Intercept Model
. mixed symptoms , ///
> || personid: , variance mle covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -721.48286
Iteration 1: log likelihood = -721.48286
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(0) = .
Log likelihood = -721.48286 Prob > chi2 = .
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | 1.293954 .1120371 11.55 0.000 1.074365 1.513542
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.189301 .183946 .8782918 1.610441
-----------------------------+------------------------------------------------
var(Residual) | .616175 .0434617 .5366175 .7075274
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 286.52 Prob >= chibar2 = 0.0000
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -721.4829 3 1448.966 1456.928
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. estat icc,
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid | .6587189 .0390572 .5786112 .7306859
------------------------------------------------------------------------------
. estat wcorrelation, covariance,
Covariances for personid = 102:
obs | 1 2 3 4 5
-------------+----------------------------------------
1 | 1.805
2 | 1.189 1.805
3 | 1.189 1.189 1.805
4 | 1.189 1.189 1.189 1.805
5 | 1.189 1.189 1.189 1.189 1.805
. estat wcorrelation,
Standard deviations and correlations for personid = 102:
Standard deviations:
obs | 1 2 3 4 5
-------------+----------------------------------------
sd | 1.344 1.344 1.344 1.344 1.344
Correlations:
obs | 1 2 3 4 5
-------------+----------------------------------------
1 | 1.000
2 | 0.659 1.000
3 | 0.659 0.659 1.000
4 | 0.659 0.659 0.659 1.000
5 | 0.659 0.659 0.659 0.659 1.000
. estimates store FitEmpty,
.
. display as result "Ch 7a: Testing Saturated Means by Day of Study"
Ch 7a: Testing Saturated Means by Day of Study
. display as result "Random Intercept Only"
Random Intercept Only
. mixed symptoms i.studyday, ///
> || personid: , variance mle covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -717.4961
Iteration 1: log likelihood = -717.4961
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(13) = 8.04
Log likelihood = -717.4961 Prob > chi2 = 0.8410
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
studyday |
2 | .0649345 .1313665 0.49 0.621 -.1925392 .3224082
3 | -.0642588 .1687662 -0.38 0.703 -.3950344 .2665168
4 | .1880234 .1956424 0.96 0.337 -.1954287 .5714755
5 | .0412025 .1860802 0.22 0.825 -.3235079 .405913
6 | .1177615 .1494617 0.79 0.431 -.1751781 .410701
7 | .0546413 .1334038 0.41 0.682 -.2068253 .3161079
8 | -.0233639 .1268237 -0.18 0.854 -.2719337 .2252059
9 | -.1800966 .1620194 -1.11 0.266 -.4976487 .1374555
10 | .191898 .1923642 1.00 0.318 -.1851288 .5689248
11 | -.305342 .281032 -1.09 0.277 -.8561546 .2454706
12 | -.0357739 .2491565 -0.14 0.886 -.5241116 .4525638
13 | -.0908273 .2491046 -0.36 0.715 -.5790633 .3974088
14 | -.2593001 .2445764 -1.06 0.289 -.7386611 .2200609
|
_cons | 1.286923 .1307181 9.85 0.000 1.03072 1.543126
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.181286 .182952 .8720167 1.60024
-----------------------------+------------------------------------------------
var(Residual) | .6053631 .0427253 .5271569 .6951716
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 284.02 Prob >= chibar2 = 0.0000
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -717.4961 16 1466.992 1509.456
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. contrast i.studyday,
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
symptoms |
studyday | 13 8.04 0.8410
------------------------------------------------
. margins i.studyday,
Adjusted predictions Number of obs = 509
Expression : Linear prediction, fixed portion, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
studyday |
1 | 1.286923 .1307181 9.85 0.000 1.03072 1.543126
2 | 1.351858 .1506917 8.97 0.000 1.056508 1.647208
3 | 1.222664 .1842287 6.64 0.000 .8615829 1.583746
4 | 1.474947 .2090974 7.05 0.000 1.065123 1.88477
5 | 1.328126 .1997736 6.65 0.000 .9365768 1.719675
6 | 1.404685 .1664002 8.44 0.000 1.078546 1.730823
7 | 1.341565 .1522341 8.81 0.000 1.043191 1.639938
8 | 1.263559 .1467232 8.61 0.000 .9759871 1.551132
9 | 1.106827 .1780593 6.22 0.000 .7578368 1.455817
10 | 1.478821 .2060714 7.18 0.000 1.074929 1.882714
11 | .9815813 .2905867 3.38 0.001 .4120419 1.551121
12 | 1.251149 .2598247 4.82 0.000 .7419024 1.760396
13 | 1.196096 .2598201 4.60 0.000 .686858 1.705334
14 | 1.027623 .2554936 4.02 0.000 .5268648 1.528381
------------------------------------------------------------------------------
. margins i.studyday, pwcompare(pveffects)
Pairwise comparisons of adjusted predictions
Expression : Linear prediction, fixed portion, predict()
-----------------------------------------------------
| Delta-method Unadjusted
| Contrast Std. Err. z P>|z|
-------------+---------------------------------------
studyday |
2 vs 1 | .0649345 .1313665 0.49 0.621
3 vs 1 | -.0642588 .1687662 -0.38 0.703
4 vs 1 | .1880234 .1956424 0.96 0.337
5 vs 1 | .0412025 .1860802 0.22 0.825
6 vs 1 | .1177615 .1494617 0.79 0.431
7 vs 1 | .0546413 .1334038 0.41 0.682
8 vs 1 | -.0233639 .1268237 -0.18 0.854
9 vs 1 | -.1800966 .1620194 -1.11 0.266
10 vs 1 | .191898 .1923642 1.00 0.318
11 vs 1 | -.305342 .281032 -1.09 0.277
12 vs 1 | -.0357739 .2491565 -0.14 0.886
13 vs 1 | -.0908273 .2491046 -0.36 0.715
14 vs 1 | -.2593001 .2445764 -1.06 0.289
3 vs 2 | -.1291933 .1833364 -0.70 0.481
4 vs 2 | .1230888 .2083223 0.59 0.555
5 vs 2 | -.023732 .204183 -0.12 0.907
6 vs 2 | .0528269 .1682802 0.31 0.754
7 vs 2 | -.0102932 .153328 -0.07 0.946
8 vs 2 | -.0882985 .1472839 -0.60 0.549
9 vs 2 | -.2450311 .177889 -1.38 0.168
10 vs 2 | .1269635 .2073994 0.61 0.540
11 vs 2 | -.3702765 .2919777 -1.27 0.205
12 vs 2 | -.1007084 .2636231 -0.38 0.702
13 vs 2 | -.1557618 .2618625 -0.59 0.552
14 vs 2 | -.3242347 .2577307 -1.26 0.208
4 vs 3 | .2522822 .2309504 1.09 0.275
5 vs 3 | .1054613 .2306733 0.46 0.648
6 vs 3 | .1820203 .2039437 0.89 0.372
7 vs 3 | .1189001 .1873571 0.63 0.526
8 vs 3 | .0408949 .1830826 0.22 0.823
9 vs 3 | -.1158378 .2066114 -0.56 0.575
10 vs 3 | .2561568 .2316284 1.11 0.269
11 vs 3 | -.2410832 .3057441 -0.79 0.430
12 vs 3 | .0284849 .2853531 0.10 0.920
13 vs 3 | -.0265685 .2847462 -0.09 0.926
14 vs 3 | -.1950413 .2781578 -0.70 0.483
5 vs 4 | -.1468208 .2431978 -0.60 0.546
6 vs 4 | -.0702619 .2238191 -0.31 0.754
7 vs 4 | -.1333821 .2132498 -0.63 0.532
8 vs 4 | -.2113873 .2088075 -1.01 0.311
9 vs 4 | -.36812 .2332127 -1.58 0.114
10 vs 4 | .0038746 .2532711 0.02 0.988
11 vs 4 | -.4933653 .32041 -1.54 0.124
12 vs 4 | -.2237973 .3025634 -0.74 0.459
13 vs 4 | -.2788506 .3014346 -0.93 0.355
14 vs 4 | -.4473235 .2994554 -1.49 0.135
6 vs 5 | .0765589 .2088338 0.37 0.714
7 vs 5 | .0134388 .2011133 0.07 0.947
8 vs 5 | -.0645665 .1985366 -0.33 0.745
9 vs 5 | -.2212991 .2252692 -0.98 0.326
10 vs 5 | .1506955 .2503606 0.60 0.547
11 vs 5 | -.3465445 .322005 -1.08 0.282
12 vs 5 | -.0769764 .2824081 -0.27 0.785
13 vs 5 | -.1320298 .2951325 -0.45 0.655
14 vs 5 | -.3005027 .2917648 -1.03 0.303
7 vs 6 | -.0631201 .1676589 -0.38 0.707
8 vs 6 | -.1411254 .1616283 -0.87 0.383
9 vs 6 | -.2978581 .1952228 -1.53 0.127
10 vs 6 | .0741365 .2219176 0.33 0.738
11 vs 6 | -.4231034 .3023503 -1.40 0.162
12 vs 6 | -.1535354 .2679717 -0.57 0.567
13 vs 6 | -.2085887 .2690775 -0.78 0.438
14 vs 6 | -.3770616 .2709644 -1.39 0.164
8 vs 7 | -.0780052 .1474815 -0.53 0.597
9 vs 7 | -.2347379 .1820014 -1.29 0.197
10 vs 7 | .1372567 .2115156 0.65 0.516
11 vs 7 | -.3599833 .295901 -1.22 0.224
12 vs 7 | -.0904152 .2621495 -0.34 0.730
13 vs 7 | -.1454686 .2633286 -0.55 0.581
14 vs 7 | -.3139414 .2565165 -1.22 0.221
9 vs 8 | -.1567327 .1765997 -0.89 0.375
10 vs 8 | .2152619 .2054159 1.05 0.295
11 vs 8 | -.281978 .292143 -0.97 0.334
12 vs 8 | -.01241 .2583705 -0.05 0.962
13 vs 8 | -.0674633 .2612481 -0.26 0.796
14 vs 8 | -.2359362 .2568273 -0.92 0.358
10 vs 9 | .3719946 .2255788 1.65 0.099
11 vs 9 | -.1252454 .3045753 -0.41 0.681
12 vs 9 | .1443227 .2787547 0.52 0.605
13 vs 9 | .0892693 .2769179 0.32 0.747
14 vs 9 | -.0792035 .2728678 -0.29 0.772
11 vs 10 | -.49724 .3205613 -1.55 0.121
12 vs 10 | -.2276719 .3013952 -0.76 0.450
13 vs 10 | -.2827253 .2935172 -0.96 0.335
14 vs 10 | -.4511981 .2917033 -1.55 0.122
12 vs 11 | .2695681 .3611986 0.75 0.455
13 vs 11 | .2145147 .3604393 0.60 0.552
14 vs 11 | .0460419 .3576197 0.13 0.898
13 vs 12 | -.0550534 .3370198 -0.16 0.870
14 vs 12 | -.2235262 .3316323 -0.67 0.500
14 vs 13 | -.1684729 .3170431 -0.53 0.595
-----------------------------------------------------
.
. display as result "Ch 7a: Testing Fixed Linear Effect of Day of Study"
Ch 7a: Testing Fixed Linear Effect of Day of Study
. display as result "Random Intercept Only"
Random Intercept Only
. mixed symptoms c.studyday1, ///
> || personid: , variance mle covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -721.07808
Iteration 1: log likelihood = -721.07808
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(1) = 0.81
Log likelihood = -721.07808 Prob > chi2 = 0.3680
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
studyday1 | -.00893 .0099197 -0.90 0.368 -.0283723 .0105122
_cons | 1.335096 .121011 11.03 0.000 1.097918 1.572273
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.18996 .1839956 .8788544 1.611195
-----------------------------+------------------------------------------------
var(Residual) | .614894 .0433711 .5355023 .706056
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 287.13 Prob >= chibar2 = 0.0000
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -721.0781 4 1450.156 1460.772
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. estimates store FitFixDayofStudy,
.
. display as result "Ch 7a: Testing Random Linear Effect of Day of Study"
Ch 7a: Testing Random Linear Effect of Day of Study
. mixed symptoms c.studyday1, ///
> || personid: studyday1, variance mle covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -720.30648
Iteration 1: log likelihood = -720.08666
Iteration 2: log likelihood = -720.08637
Iteration 3: log likelihood = -720.08637
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(1) = 0.60
Log likelihood = -720.08637 Prob > chi2 = 0.4386
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
studyday1 | -.0083746 .0108113 -0.77 0.439 -.0295643 .0128152
_cons | 1.333354 .1210305 11.02 0.000 1.096139 1.57057
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(studyd~1) | .0019996 .0016602 .0003928 .0101784
var(_cons) | 1.203731 .215703 .8472238 1.710255
cov(studyd~1,_cons) | -.0050188 .014841 -.0341067 .0240691
-----------------------------+------------------------------------------------
var(Residual) | .58349 .0464096 .4992643 .6819244
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 289.12 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -720.0864 6 1452.173 1468.096
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. estimates store FitRandDayofStudy,
. lrtest FitRandDayofStudy FitFixDayofStudy,
Likelihood-ratio test LR chi2(2) = 1.98
(Assumption: FitFixDayofS~y nested in FitRandDayof~y) Prob > chi2 = 0.3709
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Ch 7a: Testing Saturated Means by Day of Week"
Ch 7a: Testing Saturated Means by Day of Week
. display as result "Random Intercept Only"
Random Intercept Only
. mixed symptoms i.dayofweek, ///
> || personid: , variance mle covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -721.14987
Iteration 1: log likelihood = -721.14987
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(6) = 0.67
Log likelihood = -721.14987 Prob > chi2 = 0.9952
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dayofweek |
2 | -.0147541 .1886514 -0.08 0.938 -.384504 .3549959
3 | -.0428198 .1903809 -0.22 0.822 -.4159595 .3303199
4 | .0151205 .1678102 0.09 0.928 -.3137814 .3440225
5 | -.0517181 .1555261 -0.33 0.739 -.3565436 .2531074
6 | -.0624108 .1317641 -0.47 0.636 -.3206637 .1958421
7 | -.0721049 .1435154 -0.50 0.615 -.35339 .2091802
|
_cons | 1.337115 .1572183 8.50 0.000 1.028973 1.645258
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.189076 .1841042 .8778464 1.610649
-----------------------------+------------------------------------------------
var(Residual) | .6152118 .0434067 .5357565 .7064506
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 284.41 Prob >= chibar2 = 0.0000
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -721.1499 9 1460.3 1484.185
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. contrast i.dayofweek,
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
symptoms |
dayofweek | 6 0.67 0.9952
------------------------------------------------
. margins i.dayofweek,
Adjusted predictions Number of obs = 509
Expression : Linear prediction, fixed portion, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dayofweek |
1 | 1.337115 .1572183 8.50 0.000 1.028973 1.645258
2 | 1.322361 .1863984 7.09 0.000 .9570271 1.687695
3 | 1.294296 .1781142 7.27 0.000 .9451981 1.643393
4 | 1.352236 .1558551 8.68 0.000 1.046765 1.657706
5 | 1.285397 .1458217 8.81 0.000 .999592 1.571203
6 | 1.274704 .1229243 10.37 0.000 1.033777 1.515632
7 | 1.26501 .1372873 9.21 0.000 .9959323 1.534088
------------------------------------------------------------------------------
. margins i.dayofweek, pwcompare(pveffects)
Pairwise comparisons of adjusted predictions
Expression : Linear prediction, fixed portion, predict()
-----------------------------------------------------
| Delta-method Unadjusted
| Contrast Std. Err. z P>|z|
-------------+---------------------------------------
dayofweek |
2 vs 1 | -.0147541 .1886514 -0.08 0.938
3 vs 1 | -.0428198 .1903809 -0.22 0.822
4 vs 1 | .0151205 .1678102 0.09 0.928
5 vs 1 | -.0517181 .1555261 -0.33 0.739
6 vs 1 | -.0624108 .1317641 -0.47 0.636
7 vs 1 | -.0721049 .1435154 -0.50 0.615
3 vs 2 | -.0280657 .2098616 -0.13 0.894
4 vs 2 | .0298746 .1944615 0.15 0.878
5 vs 2 | -.036964 .187232 -0.20 0.843
6 vs 2 | -.0476567 .1661742 -0.29 0.774
7 vs 2 | -.0573508 .1763767 -0.33 0.745
4 vs 3 | .0579403 .1809791 0.32 0.749
5 vs 3 | -.0088983 .17515 -0.05 0.959
6 vs 3 | -.0195911 .1562362 -0.13 0.900
7 vs 3 | -.0292852 .171795 -0.17 0.865
5 vs 4 | -.0668386 .1515546 -0.44 0.659
6 vs 4 | -.0775314 .1294294 -0.60 0.549
7 vs 4 | -.0872255 .1454729 -0.60 0.549
6 vs 5 | -.0106928 .117083 -0.09 0.927
7 vs 5 | -.0203869 .1336603 -0.15 0.879
7 vs 6 | -.0096941 .1064634 -0.09 0.927
-----------------------------------------------------
.
. display as result "Ch 7a: Testing Fixed Effect of Weekend"
Ch 7a: Testing Fixed Effect of Weekend
. display as result "Random Intercept Only"
Random Intercept Only
. mixed symptoms c.weekend, ///
> || personid: , variance mle covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -721.28173
Iteration 1: log likelihood = -721.28173
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(1) = 0.40
Log likelihood = -721.28173 Prob > chi2 = 0.5257
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weekend | -.0464164 .0731406 -0.63 0.526 -.1897694 .0969366
_cons | 1.317625 .1181543 11.15 0.000 1.086047 1.549204
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.191385 .1842377 .879875 1.613182
-----------------------------+------------------------------------------------
var(Residual) | .6153304 .0434037 .5358793 .7065613
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 286.91 Prob >= chibar2 = 0.0000
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -721.2817 4 1450.563 1461.179
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. estimates store FitFixWeekend,
.
. display as result "Ch 7a: Testing Random Effect of Weekend"
Ch 7a: Testing Random Effect of Weekend
. mixed symptoms c.weekend, ///
> || personid: weekend, variance mle covariance(unstructured),
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -722.71893
Iteration 1: log likelihood = -721.1791
Iteration 2: log likelihood = -721.14497
Iteration 3: log likelihood = -721.14481
Iteration 4: log likelihood = -721.14481
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(1) = 0.41
Log likelihood = -721.14481 Prob > chi2 = 0.5234
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weekend | -.046703 .0731957 -0.64 0.523 -.190164 .0967579
_cons | 1.318414 .1200422 10.98 0.000 1.083136 1.553692
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Unstructured |
var(weekend) | .0016219 .0010806 .0004395 .0059863
var(_cons) | 1.23837 .1877832 .9199758 1.666957
cov(weekend,_cons) | -.044817 .0152206 -.0746489 -.0149852
-----------------------------+------------------------------------------------
var(Residual) | .6146827 .0464119 .5301279 .7127238
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 287.18 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -721.1448 6 1454.29 1470.213
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. estimates store FitRandWeekend,
. lrtest FitRandWeekend FitFixWeekend,
Likelihood-ratio test LR chi2(2) = 0.27
(Assumption: FitFixWeekend nested in FitRandWeekend) Prob > chi2 = 0.8720
Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space. If this is not true, then the
reported test is conservative.
.
. display as result "Eq 7a.4: Adding Sex and Age to the Model for the Means"
Eq 7a.4: Adding Sex and Age to the Model for the Means
. mixed symptoms c.women c.age80 c.women#c.age80, ///
> || personid: , variance mle covariance(unstructured),
Note: single-variable random-effects specification in personid equation; covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -716.28897
Iteration 1: log likelihood = -716.28897
Computing standard errors:
Mixed-effects ML regression Number of obs = 509
Group variable: personid Number of groups = 105
Obs per group: min = 2
avg = 4.8
max = 5
Wald chi2(3) = 10.85
Log likelihood = -716.28897 Prob > chi2 = 0.0126
---------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
women | -.5306419 .2451324 -2.16 0.030 -1.011093 -.0501912
age80 | .0999995 .0370575 2.70 0.007 .0273681 .1726309
|
c.women#c.age80 | -.1104279 .0422013 -2.62 0.009 -.1931409 -.027715
|
_cons | 1.712739 .2107731 8.13 0.000 1.299632 2.125847
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity |
var(_cons) | 1.072738 .1667213 .7910477 1.454737
-----------------------------+------------------------------------------------
var(Residual) | .6151891 .0433293 .5358663 .706254
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 271.56 Prob >= chibar2 = 0.0000
. estat ic, n(105),
Akaike's information criterion and Bayesian information criterion
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 105 . -716.289 6 1444.578 1460.502
-----------------------------------------------------------------------------
Note: N=105 used in calculating BIC
. estat vce,
Covariance matrix of coefficients of mixed model
| symptoms | lns1_1_1 | lnsig_e
| c.women# | |
e(V) | women age80 c.age80 _cons | _cons | _cons
-------------+------------------------------------------------+------------+------------
symptoms | | |
women | .0600899 | |
age80 | -.00131503 .00137326 | |
c.women#| | |
c.age80 | .00111354 -.00137326 .00178095 | |
_cons | -.04442528 .00131503 -.00131503 .04442528 | |
-------------+------------------------------------------------+------------+------------
lns1_1_1 | | |
_cons | 0 0 0 0 | .00603859 |
-------------+------------------------------------------------+------------+------------
lnsig_e | | |
_cons | 0 0 0 0 | -.00015954 | .00124018
. * Multivariate Test of Fixed Effects
. test (c.women=0) (c.age80=0) (c.women#c.age80=0)
( 1) [symptoms]women = 0
( 2) [symptoms]age80 = 0
( 3) [symptoms]c.women#c.age80 = 0
chi2( 3) = 10.85
Prob > chi2 = 0.0126
. * Age Slope for Men
. lincom c.age80*1 + c.women#c.age80*0
( 1) [symptoms]age80 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .0999995 .0370575 2.70 0.007 .0273681 .1726309
------------------------------------------------------------------------------
. * Age Slope for Women
. lincom c.age80*1 + c.women#c.age80*1
( 1) [symptoms]age80 + [symptoms]c.women#c.age80 = 0
------------------------------------------------------------------------------
symptoms | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.0104285 .0201913 -0.52 0.606 -.0500027 .0291457
------------------------------------------------------------------------------
. estimates store FitSexAge,
. lrtest FitSexAge FitEmpty,
Likelihood-ratio test LR chi2(3) = 10.39
(Assumption: FitEmpty nested in FitSexAge) Prob > chi2 = 0.0155
. predict PredSexAge, xb,
. corr symptoms PredSexAge
(obs=509)
| symptoms PredSe~e
-------------+------------------
symptoms | 1.0000
PredSexAge | 0.2201 1.0000
.
. ****** END CHAPTER 7a MODELS ******
.
. * Close log
. log close STATA_Chapter7a
name: STATA_Chapter7a
log: C:\Dropbox\PilesOfVariance\Chapter7a\STATA\STATA_Chapter7a_Output.smcl
log type: smcl
closed on: 12 Jan 2015, 10:30:57
------------------------------------------------------------------------------------------------------------------------------------------------------