PSC 8185: Multilevel Modeling Fitting Random Coefficient Binary Response Models in Stata
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1 PSC 8185: Multilevel Modeling Fitting Random Coefficient Binary Response Models in Stata Consider the following two-level model random coefficient logit model. This is a Supreme Court decision making model, where level-1 units are justices votes and level-2 units are court cases (justices votes (3544) nested within 399 cases). For binary dependent variables, a Bernoulli sampling model is used, and I use a logit link here. For the logit link, first define Pr(Y ij =1) = p ij, which is the probability of a liberal vote for choice i in case j. Then define ij as the log-odds of p ij : ij = log[p ij / (1 p ij )]. This allows one to specify the log-odds as a linear function of the level-1 independent variables. [Level-1 eq.] [Level-2 eqs.] ij = 0j + j PREF ij 0j = SAL j + 02 COMP j + 03 ISSUEFAM j + 04 INFO j + 05 USAMICUS j + 06 USPARTY j + 07 STAT j + u 0j j = SAL j + 12 COMP j + 13 ISSUEFAM j + 14 INFO j + 15 USAMICUS j + 16 USPARTY j + 17 STAT j + u 1j Reduced-form Representation of Model 2: ij = Effects on case outcome Avg. effect of preferences Cross-level interactions Error components SAL j + 02 COMP j + 03 ISSUEFAM j + 04 INFO j + 05 USAMICUS j + 06 USPARTY j + 07 STAT j + 10 *PREF ij + 11 SAL j *PREF ij + 12 COMP j *PREF ij + 13 ISSUEFAM j*pref ij + 14 INFO j *PREF ij + 15 USAMICUS j *PREF ij + 16 USPARTY j *PREF ij + 17 STAT j *PREF ij + u 0j + u 1j *PREF ij 1
2 Fitting the Two-Level Model using Full Maximum Likelihood (Adaptive Quadrature) in GLLAMM set more off *ADAPTIVE QUADRATURE MODELS *Generate a constant; gllamm needs this gen cons=1 *Specify random intercept and random coefficient eq cons: cons eq pref: lagpctlib_use *Specify the level-2 variables that are a function of the random intercept eq f1: salience_nyt_cen complex_3pt_cen lnissuecount_cen infoenv_01_cen usamicus_cen usparty_cen statutory_cen *Specify the level-2 variables that are a function of the random coefficient eq f2: salience_nyt_cen complex_3pt_cen lnissuecount_cen infoenv_01_cen usamicus_cen usparty_cen statutory_cen *Model command; start with 4 quadrature points, then 8, then 12, etc.; use *start values from the previous model (that s the from(a) command) geqs(f1 f2) adapt nip(4) geqs(f1 f2) adapt nip(8) from(a) geqs(f1 f2) adapt nip(12) from(a) est store lag_adapt12 geqs(f1 f2) adapt nip(16) from(a) est store lag_adapt16 geqs(f1 f2) adapt nip(20) from(a) est store lag_adapt20 *Present results in a table form est table lag_adapt12 lag_adapt16 lag_adapt20, se p varwidth(34) stats(n ll aic) 2
3 . *ADAPTIVE QUADRATURE MODELS GLLAMM OUTPUT [Suppressing output from models using 4 and 8 quadrature points.]. gllamm dir lagpctlib_use if lagpctlib_use~=., i(caseid) l(logit) f(binom) nrf(2) eqs(cons pref) geqs(f1 f2) adapt nip (12) from(a) Running adaptive quadrature Iteration 0: log likelihood = Iteration 1: log likelihood = Iteration 2: log likelihood = Adaptive quadrature has converged, running Newton-Raphson Iteration 0: log likelihood = Iteration 1: log likelihood = (backed up) Iteration 2: log likelihood = Iteration 3: log likelihood = number of level 1 units = 3544 number of level 2 units = 399 Condition Number = gllamm model log likelihood = dir Coef. Std. Err. z P> z [95% Conf. Interval] lagpctlib_~e _cons Variances and covariances of random effects ***level 2 (caseid) var(1): ( ) cov(2,1): ( ) cor(2,1): var(2): ( ) Regressions of latent variables on covariates random effect 1 has 7 covariates: salience_nyt_cen: ( ) complex_3pt_cen: ( ) lnissuecount_cen: ( ) infoenv_01_cen: ( ) usamicus_cen: ( ) usparty_cen: ( ) statutory_cen: ( ) 3
4 random effect 2 has 7 covariates: salience_nyt_cen: ( ) complex_3pt_cen: ( ) lnissuecount_cen: ( ) infoenv_01_cen: ( ) usamicus_cen: ( ) usparty_cen: ( ) statutory_cen: ( ). est store lag_adapt12 [Suppressing output from models using 16 and 20 quadrature points.].. est table lag_adapt12 lag_adapt16 lag_adapt20, se p varwidth(34) stats(n ll aic) Variable lag_ada~12 lag_ada~16 lag_ada~20 dir lagpctlib_use _cons cas1_1 cons cas1_2 lagpctlib_use cas1_2_1 _cons f1 salience_nyt_cen complex_3pt_cen lnissuecount_cen infoenv_01_cen usamicus_cen
5 usparty_cen statutory_cen f2 salience_nyt_cen complex_3pt_cen lnissuecount_cen infoenv_01_cen usamicus_cen usparty_cen statutory_cen Statistics N ll aic legend: b/se/p 5
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