Nd were not involved in gangs, we tested interactions of our dichotomous indicator of ever or never a gang member with each of our 15 covariates. Because of the large number of individual tests, we first tested the joint significance of this set of interactions based on an F test (combining estimates with Rubin’s rules). As noted, the multinomial logit model produces a set of coefficients for all but the reference outcomeNIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author ManuscriptJ Res Adolesc. Author manuscript; available in PMC 2015 June 01.Gordon et al.Pagecategory–seven sets of interactions given our eight outcome categories–and thus there were 7?5=105 interactions in all (and thus 105 numerator degrees of freedom for this F test). After obtaining a significant overall F test, we then used additional F tests to see which covariates had significant interactions, first jointly testing the seven interaction terms for each covariate and then considering which individual interaction terms were significant. We also estimated a “main effects” multinomial logit model (without interactions) and calculated an F value to test whether the covariate’s main effect was 5-BrdU biological activity statistically significant across the seven equations (this F value had 7 numerator degrees of freedom). In addition to these multinomial logit models, we also estimated a logit model with active gang membership in the reference period before the current study wave as the outcome and our 15 covariates. Because there is only one equation for these logit models, the relevant F tests for each of the 15 covariates has just one numerator degree of freedom. For both the outcomes of configurations of serious delinquency and of active gang membership, we also tested for interactions by the three time dimensions in our data: youth’s age, historical period, and cohort. Doing so provided statistical justification for combining the two PYS cohorts in a single analysis. It also allowed us to examine whether developmental patterns of combining the three types of serious delinquency and of participating in gangs depended on our covariates (e.g., differed for Black and non-Black youth or for boys living with both biological parents FCCPMedChemExpress FCCP versus one or no biological parents) and whether covariates likewise moderated time trends across calendar year in these activities. To facilitate interpretation, we calculated the predicted probability of youth occupying each outcome category. For significant covariates, Figures S1 12 of the online supporting information graph these predicted probabilities, which we summarize in the text below. We used predicted probabilities for interpretation because logit models are inherently non-linear and because the substantive size of statistically significant associations is more meaningful in probability than odds units (Long, 1997; Long Freese, 2003). We made these calculations repeatedly, selecting a value of interest for a particular variable (e.g., our focal covariate of gang membership) and holding the remaining covariates constant at their means.NIH-PA Author Manuscript NIH-PA Author Manuscript Results NIH-PA Author ManuscriptDescribing Configurations of Serious Delinquency among Delinquent Young Men Who Were and Were Not Gang-Involved Table 2 provides the percentage of waves at which youth reported having engaged in drug selling, serious theft, and serious violence since the last interview, among all youth and by gang membership status (never in a gang.Nd were not involved in gangs, we tested interactions of our dichotomous indicator of ever or never a gang member with each of our 15 covariates. Because of the large number of individual tests, we first tested the joint significance of this set of interactions based on an F test (combining estimates with Rubin’s rules). As noted, the multinomial logit model produces a set of coefficients for all but the reference outcomeNIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author ManuscriptJ Res Adolesc. Author manuscript; available in PMC 2015 June 01.Gordon et al.Pagecategory–seven sets of interactions given our eight outcome categories–and thus there were 7?5=105 interactions in all (and thus 105 numerator degrees of freedom for this F test). After obtaining a significant overall F test, we then used additional F tests to see which covariates had significant interactions, first jointly testing the seven interaction terms for each covariate and then considering which individual interaction terms were significant. We also estimated a “main effects” multinomial logit model (without interactions) and calculated an F value to test whether the covariate’s main effect was statistically significant across the seven equations (this F value had 7 numerator degrees of freedom). In addition to these multinomial logit models, we also estimated a logit model with active gang membership in the reference period before the current study wave as the outcome and our 15 covariates. Because there is only one equation for these logit models, the relevant F tests for each of the 15 covariates has just one numerator degree of freedom. For both the outcomes of configurations of serious delinquency and of active gang membership, we also tested for interactions by the three time dimensions in our data: youth’s age, historical period, and cohort. Doing so provided statistical justification for combining the two PYS cohorts in a single analysis. It also allowed us to examine whether developmental patterns of combining the three types of serious delinquency and of participating in gangs depended on our covariates (e.g., differed for Black and non-Black youth or for boys living with both biological parents versus one or no biological parents) and whether covariates likewise moderated time trends across calendar year in these activities. To facilitate interpretation, we calculated the predicted probability of youth occupying each outcome category. For significant covariates, Figures S1 12 of the online supporting information graph these predicted probabilities, which we summarize in the text below. We used predicted probabilities for interpretation because logit models are inherently non-linear and because the substantive size of statistically significant associations is more meaningful in probability than odds units (Long, 1997; Long Freese, 2003). We made these calculations repeatedly, selecting a value of interest for a particular variable (e.g., our focal covariate of gang membership) and holding the remaining covariates constant at their means.NIH-PA Author Manuscript NIH-PA Author Manuscript Results NIH-PA Author ManuscriptDescribing Configurations of Serious Delinquency among Delinquent Young Men Who Were and Were Not Gang-Involved Table 2 provides the percentage of waves at which youth reported having engaged in drug selling, serious theft, and serious violence since the last interview, among all youth and by gang membership status (never in a gang.
