Normative Developmental Trajectories of Aggressive Behaviors in African American, American Indian, Asian American, Caucasian, and Hispanic Children and Early Adolescents

Children are nested in different SES strata; thus, modeling individual nesting effects might provide finer and perhaps better tests of SES effects. However, because only four strata ranging from low SES to lower–middle SES were developed, differentiating potential effects within this highly restricted range did not appear to be salient, and of course, analytically, it was a challenge due to the small number of strata.

We also need to acknowledge an additional level of nesting in the data, namely students located within schools; this provides another source of potential variability in the tested relationships and developmental processes, but also one for an increased probability of Type I errors due to underestimates of the standard errors. However, because of study design features (all convenience samples of entire schools located in the same general vicinity in the original sample of 8 schools), the small number of schools for most data collection periods of the original 8 schools (which limits the ability to complete multi-level models), and because of the complexity of the LGM approach used, no “true” multi-level analytic approach was employed to model school-level nesting effects. However, in an effort to deal with the issue and to examine whether student nesting effects in schools were related to the growth parameters, a model with dummy coded variables representing the schools as the sole set of predictors was tested. Findings provided evidence that the model with the schools entered as predictors (BIC = 26,689 and adj. BIC = 26,518) fit the data less well than the model without the school predictors (BIC = 26,631 and adj. BIC = 26,510). In addition, school effect variables accounted for a mere 0.1% to 0.3% of the variance in the growth parameters.

The fitted equation for the estimation of the growth in the probability of use versus non-use of aggression is a logistic regression model, 1 / (1 + e ^{−(i+s*t+q*t**2)}).

Prior to setting the variances to zero, we did fit a model testing the significance of the ethnicity variables in predicting the slopes and quadratic terms of frequency and prevalence of aggression. The effects of ethnicity were not significant.

The fitted equation for the estimation of the growth in the probability of use versus non-use of aggression is a logistic regression model, 1 / (1 + e ^{−((i+b1*x1+b2*x2+...+bn *xn ) + s*t.+q*(t**2))}). The fitted equation for the estimation of the growth in the frequency of non-zero aggression is the usual linear growth model, (i + b ₁ x ₁ + b ₂ x ₂ + ... + b _n x _n) + s*t. + q*(t**2).