Estimation of the p covariate coefficients α, the population variance-covariance parameters Λ (with r(r+1)/2 elements), and the (h + 1)(K –1) parameters in γk (k = 1, …, K – 1) is described in detail by Hedeker and Gibbons (1994).
To illustrate application of the mixed-effects ordinal logistic regression model, we reanalyzed longitudinal data from Rudd et al. (1996) on suicidal ideation and attempts in a sample of 300 suicidal young adults (personal communication, M.D. Rudd, Baylor University, October 2001). 180 subjects were assigned to an outpatient intervention group therapy condition and 120 subjects received treatment as usual. In this analysis, we used an ordinal outcome measure of 0=low suicidal ideation, 1=clinically significant suicidal ideation, and 3=suicide attempt. Suicidal ideation was defined as a score of 11 or more on the Modified Scale for Suicide Ideation (MSSI; Miller et al., 1986). Model specification included main effects of month (0, 1, and 6) and treatment (0=control, 1=intervention), and the treatment by month interaction. Although data at 12, 18 and 24 months were also available, the drop-out rates at these later months were too large for a meaningful analysis. In addition, to illustrate the flexibility of the model, depression as measured by the Beck Depression Inventory (BDI; Beck and Steer, 1987) and anxiety as measured by the Millon Clinical Multiaxial Inventory (MCMI-A; Millon, 1983) were treated as time-varying covariates in the model, to relate fluctuations in depressed mood and anxiety to shifts in suicidality.
Table A-5 displays the observed proportions in each of the three ordinal suicide categories as a function of month and treatment. Table A-5 reveals that, if anything, the observed rate of attempts is as high or higher in the intervention group than the control group. Note that this is also true at baseline, therefore, these difference may be an artifact of randomization.
Table A-6 displays the model parameter estimates, standard errors, and associated probability estimates. A model with both random intercept and slope (i.e., month) effects failed to converge because the variance component for the intercept was close to zero. In light of this, the model was specified with a single random effect (i.e., a random slope model). Table A-6 reveals that both of the time-varying covariates, depression and anxiety, were significantly associated with suicidality. By contrast, the treatment by time interaction was not significant, indicating that the intervention did not significantly affect the rates suicide ideation or at-