distribution of Bayes estimates for outliers. For example, in the western continental United States and Alaska where suicide rates are typically high, a few counties have Bayes estimates consistent with the national average. Similarly, in the central United States where there is a high concentration of counties with the lowest suicide rates, a few counties exhibit the highest suicide rates. What are the risk and protective factors that have produced these spatial anomalies? Are these spatial anomalies simply due to reporting bias or some other unmeasured characteristic? Based on a review of the literature, it does not appear that this type of statistical approach to this problem has been previously considered. Examining these spatial anomalies in greater detail is a fruitful area for further research.

Mixed-effects Ordinal Regression Models

To study suicidal ideation, attempts, and completion in individual participants under various conditions, mixed-effects ordinal and nominal regression models can be used. The basic concept is to develop an ordinal scale of suicidal behavior, ranging from no suicidal ideation, low, medium, and high suicidal ideation, suicide attempt, and ending at suicide completion. Several authors have described models including both random and fixed effects (e.g., Agresti and Lang, 1993; Ezzet and Whitehead, 1991; Harville and Mee, 1984; Hedeker and Gibbons, 1994; Jansen, 1990; Ten Have, 1996). Statistical details are presented in Appendix A.

A reanalysis of the longitudinal data from Rudd et al. (1996) on suicidal ideation and attempts in a sample of 300 suicidal young adults (personal communication, Dr. M. David Rudd, Professor of Psychology, Baylor University) serves as an illustration of an application of the mixed-effects ordinal logistic regression model. In the original study, 180 participants were assigned to an outpatient intervention group therapy condition and 120 participants received treatment as usual. This re-analysis assigns the ordinal outcome measure of 0=low suicidal ideation, 1=clinically significant suicidal ideation, and 2=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 dropout 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



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