Figure 14.1 on page 211.
use snijder_chap14, clear preserve collapse (mean) cohab, by(reg) gen one = 1 gen zero = 0 twoway rspike one zero cohab, xlab(.2(.2) .8) ylab(0 5) /// plotregion(style(none)) yscale(off) ysize(1.5) xsize(4) restore
Chi-square test for equality of proportions and variance calculation on page 211.
tab cohab reg, chi2
| reg
cohab | 1 2 3 4 5 6 7 8 | Total
-----------+----------------------------------------------------------------------------------------+----------
0 | 73 102 135 41 54 58 54 48 | 1,177
1 | 34 113 100 42 37 53 44 27 | 902
-----------+----------------------------------------------------------------------------------------+----------
Total | 107 215 235 83 91 111 98 75 | 2,079
| reg
cohab | 9 10 11 12 14 15 16 17 | Total
-----------+----------------------------------------------------------------------------------------+----------
0 | 38 51 96 121 32 67 63 34 | 1,177
1 | 19 23 66 79 23 54 46 21 | 902
-----------+----------------------------------------------------------------------------------------+----------
Total | 57 74 162 200 55 121 109 55 | 2,079
| reg
cohab | 18 19 20 | Total
-----------+---------------------------------+----------
0 | 62 32 16 | 1,177
1 | 63 39 19 | 902
-----------+---------------------------------+----------
Total | 125 71 35 | 2,079
Pearson chi2(18) = 35.4000 Pr = 0.008
xtmixed cohab ||reg:, var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -1491.4981
Iteration 1: log restricted-likelihood = -1491.498
Computing standard errors:
Mixed-effects REML regression Number of obs = 2079
Group variable: reg Number of groups = 19
Obs per group: min = 35
avg = 109.4
max = 235
Wald chi2(0) = .
Log restricted-likelihood = -1491.498 Prob > chi2 = .
------------------------------------------------------------------------------
cohab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .4313919 .0157033 27.47 0.000 .4006139 .4621698
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
reg: Identity |
var(_cons) | .0021911 .0015606 .0005425 .0088501
-----------------------------+------------------------------------------------
var(Residual) | .2437321 .0075941 .2292934 .2590801
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 5.35 Prob >= chibar2 = 0.0103
Table 14.1 on page 214.
xtmelogit cohab ||reg:, var mle
Refining starting values:
Iteration 0: log likelihood = -1436.0778 (not concave)
Iteration 1: log likelihood = -1420.7298
Iteration 2: log likelihood = -1420.5007
Performing gradient-based optimization:
Iteration 0: log likelihood = -1420.5007
Iteration 1: log likelihood = -1420.4928
Iteration 2: log likelihood = -1420.4928
Mixed-effects logistic regression Number of obs = 2079
Group variable: reg Number of groups = 19
Obs per group: min = 35
avg = 109.4
max = 235
Integration points = 7 Wald chi2(0) = .
Log likelihood = -1420.4928 Prob > chi2 = .
------------------------------------------------------------------------------
cohab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | -.2778168 .0626587 -4.43 0.000 -.4006257 -.1550079
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
reg: Identity |
var(_cons) | .0324699 .0241911 .0075389 .1398473
------------------------------------------------------------------------------
LR test vs. logistic regression: chibar2(01) = 4.64 Prob>=chibar2 = 0.0156
Table 14.2 on page 217, model 1.
gen x1 = age - 20
gen x2 = (age-20)^2
gen x3 = 0
replace x3 = (age-30)^2 if age>30
gen x4 = 0
replace x4 = (age-40)^2 if age>40
xtmelogit cohab x* ||reg:, var
Refining starting values:
Iteration 0: log likelihood = -1135.7448 (not concave)
Iteration 1: log likelihood = -1123.9337
Iteration 2: log likelihood = -1123.8488
Performing gradient-based optimization:
Iteration 0: log likelihood = -1123.8488
Iteration 1: log likelihood = -1123.8486
Iteration 2: log likelihood = -1123.8486
Mixed-effects logistic regression Number of obs = 2079
Group variable: reg Number of groups = 19
Obs per group: min = 35
avg = 109.4
max = 235
Integration points = 7 Wald chi2(4) = 424.21
Log likelihood = -1123.8486 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
cohab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .5453759 .0513839 10.61 0.000 .4446653 .6460865
x2 | -.0292833 .0037238 -7.86 0.000 -.0365818 -.0219847
x3 | .0242597 .005472 4.43 0.000 .0135348 .0349846
x4 | .0068919 .0024996 2.76 0.006 .0019928 .011791
_cons | -1.214272 .1551446 -7.83 0.000 -1.51835 -.9101941
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
reg: Identity |
var(_cons) | .0627891 .0396416 .0182172 .2164145
------------------------------------------------------------------------------
LR test vs. logistic regression: chibar2(01) = 8.03 Prob>=chibar2 = 0.0023
Figure 14.6 on page 217.
predict xb, xb sort age twoway line xb age if age>=20
Table 14.2 on page 217, model 2.
gen religion = 1
replace religion = 0 if relserv >=3.5
xtmelogit cohab x* religion ||reg:, var
note: xb dropped because of collinearity
Refining starting values:
Iteration 0: log likelihood = -1098.0525 (not concave)
Iteration 1: log likelihood = -1086.0279
Iteration 2: log likelihood = -1085.6553
Performing gradient-based optimization:
Iteration 0: log likelihood = -1085.6553
Iteration 1: log likelihood = -1085.6197
Iteration 2: log likelihood = -1085.6197
Mixed-effects logistic regression Number of obs = 2079
Group variable: reg Number of groups = 19
Obs per group: min = 35
avg = 109.4
max = 235
Integration points = 7 Wald chi2(5) = 449.04
Log likelihood = -1085.6197 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
cohab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .5488541 .0519315 10.57 0.000 .4470703 .6506379
x2 | -.0291627 .0037768 -7.72 0.000 -.0365651 -.0217603
x3 | .0236239 .0055663 4.24 0.000 .0127142 .0345336
x4 | .0075683 .0025535 2.96 0.003 .0025635 .0125731
religion | -1.869635 .2430106 -7.69 0.000 -2.345927 -1.393343
_cons | -1.117111 .1537198 -7.27 0.000 -1.418396 -.815826
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
reg: Identity |
var(_cons) | .0505109 .036407 .0122988 .207448
------------------------------------------------------------------------------
LR test vs. logistic regression: chibar2(01) = 5.23 Prob>=chibar2 = 0.0111
Table 14.3 on page 222 using dataset for this table.
use table_14_3, clear
xtmelogit foe ego pfa ||respondant: pfa, var cov(un)
Refining starting values:
Iteration 0: log likelihood = -798.74841
Iteration 1: log likelihood = -791.53546
Iteration 2: log likelihood = -791.06141
Performing gradient-based optimization:
Iteration 0: log likelihood = -791.06141
Iteration 1: log likelihood = -791.05138
Iteration 2: log likelihood = -791.05138
Mixed-effects logistic regression Number of obs = 1683
Group variable: respondant Number of groups = 426
Obs per group: min = 1
avg = 4.0
max = 14
Integration points = 7 Wald chi2(2) = 1.53
Log likelihood = -791.05138 Prob > chi2 = 0.4651
------------------------------------------------------------------------------
foe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ego | .2798584 .2320657 1.21 0.228 -.174982 .7346987
pfa | -.3306332 .7571286 -0.44 0.662 -1.814578 1.153312
_cons | -1.92459 .1402628 -13.72 0.000 -2.199501 -1.64968
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
respondant: Unstructured |
var(pfa) | 5.290383 4.937787 .8492134 32.95774
var(_cons) | 1.587789 .3909177 .9799971 2.572532
cov(pfa,_cons) | -.1469777 .9823098 -2.07227 1.778314
------------------------------------------------------------------------------
LR test vs. logistic regression: chi2(3) = 62.58 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
di -2*e(ll)
1582.1028
estimates store m1
xtmelogit foe ego pfa ||respondant: , var cov(un)
Note: single-variable random-effects specification; covariance structure set to identity
Refining starting values:
Iteration 0: log likelihood = -799.52695
Iteration 1: log likelihood = -793.9659
Iteration 2: log likelihood = -793.8014
Performing gradient-based optimization:
Iteration 0: log likelihood = -793.8014
Iteration 1: log likelihood = -793.80109
Iteration 2: log likelihood = -793.80109
Mixed-effects logistic regression Number of obs = 1683
Group variable: respondant Number of groups = 426
Obs per group: min = 1
avg = 4.0
max = 14
Integration points = 7 Wald chi2(2) = 3.07
Log likelihood = -793.80109 Prob > chi2 = 0.2159
------------------------------------------------------------------------------
foe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ego | .2473459 .2169032 1.14 0.254 -.1777765 .6724683
pfa | .3176939 .2424613 1.31 0.190 -.1575216 .7929093
_cons | -1.877151 .1315776 -14.27 0.000 -2.135038 -1.619263
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
respondant: Identity |
var(_cons) | 1.403913 .3313099 .8840256 2.229541
------------------------------------------------------------------------------
LR test vs. logistic regression: chibar2(01) = 57.08 Prob>=chibar2 = 0.0000
di -2*e(ll)
1587.6022
estimates store m2
* the result is two-sided, need to adjusted to one-sided
lrtest m1 m2
Likelihood-ratio test LR chi2(2) = 5.50
(Assumption: m2 nested in m1) Prob > chi2 = 0.0639
Note: LR test is conservative
xi: xtmelogit foe i.ego*i.pfa col sup sub nei ||respondant: pfa, var cov(un)
i.ego _Iego_0-1 (naturally coded; _Iego_0 omitted)
i.pfa _Ipfa_0-1 (naturally coded; _Ipfa_0 omitted)
i.ego*i.pfa _IegoXpfa_#_# (coded as above)
Refining starting values:
Iteration 0: log likelihood = -768.38146
Iteration 1: log likelihood = -760.95373
Iteration 2: log likelihood = -760.45097
Performing gradient-based optimization:
Iteration 0: log likelihood = -760.45097
Iteration 1: log likelihood = -760.07085
Iteration 2: log likelihood = -759.9334
Iteration 3: log likelihood = -759.93322
Iteration 4: log likelihood = -759.93322
Mixed-effects logistic regression Number of obs = 1683
Group variable: respondant Number of groups = 426
Obs per group: min = 1
avg = 4.0
max = 14
Integration points = 7 Wald chi2(7) = 53.29
Log likelihood = -759.93322 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
foe | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Iego_1 | .2506568 .2388512 1.05 0.294 -.217483 .7187966
_Ipfa_1 | -.1059095 .7358454 -0.14 0.886 -1.54814 1.336321
_IegoXpfa_~1 | -1.089537 .9800973 -1.11 0.266 -3.010492 .8314183
col | 1.189454 .2338061 5.09 0.000 .7312024 1.647706
sup | 1.333307 .254923 5.23 0.000 .8336667 1.832947
sub | -.1984302 .7449843 -0.27 0.790 -1.658573 1.261712
nei | 2.299506 .3585229 6.41 0.000 1.596814 3.002198
_cons | -2.965708 .2430836 -12.20 0.000 -3.442143 -2.489273
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
respondant: Unstructured |
var(pfa) | 5.260331 5.140629 .7747848 35.71453
var(_cons) | 1.682331 .4236274 1.027 2.755829
cov(pfa,_cons) | .211198 1.03089 -1.809309 2.231705
------------------------------------------------------------------------------
LR test vs. logistic regression: chi2(3) = 60.77 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
Results listed on page 224.
use snijder_chap14, clear
xtmixed cohab ||reg:, var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log restricted-likelihood = -1491.4981
Iteration 1: log restricted-likelihood = -1491.498
Computing standard errors:
Mixed-effects REML regression Number of obs = 2079
Group variable: reg Number of groups = 19
Obs per group: min = 35
avg = 109.4
max = 235
Wald chi2(0) = .
Log restricted-likelihood = -1491.498 Prob > chi2 = .
------------------------------------------------------------------------------
cohab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .4313919 .0157033 27.47 0.000 .4006139 .4621698
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
reg: Identity |
var(_cons) | .0021911 .0015606 .0005425 .0088501
-----------------------------+------------------------------------------------
var(Residual) | .2437321 .0075941 .2292934 .2590801
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 5.35 Prob >= chibar2 = 0.0103
di exp(_b[lns1_1_1:_cons])^2 /(exp(_b[lns1_1_1:_cons])^2 + _b[cohab:_cons]*(1-_b[cohab:_cons]))
.00885335
xtmelogit cohab ||reg:, var
Refining starting values:
Iteration 0: log likelihood = -1436.0778 (not concave)
Iteration 1: log likelihood = -1420.7298
Iteration 2: log likelihood = -1420.5007
Performing gradient-based optimization:
Iteration 0: log likelihood = -1420.5007
Iteration 1: log likelihood = -1420.4928
Iteration 2: log likelihood = -1420.4928
Mixed-effects logistic regression Number of obs = 2079
Group variable: reg Number of groups = 19
Obs per group: min = 35
avg = 109.4
max = 235
Integration points = 7 Wald chi2(0) = .
Log likelihood = -1420.4928 Prob > chi2 = .
------------------------------------------------------------------------------
cohab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | -.2778168 .0626587 -4.43 0.000 -.4006257 -.1550079
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
reg: Identity |
var(_cons) | .0324699 .0241911 .0075389 .1398473
------------------------------------------------------------------------------
LR test vs. logistic regression: chibar2(01) = 4.64 Prob>=chibar2 = 0.0156
di exp(_b[lns1_1_1:_cons])^2 /(exp(_b[lns1_1_1:_cons])^2 + _pi^2/3)
.0097732