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We often encounter nonstandard conditions when trying to model psychological growth and change that go beyond the traditional growth curve framework. One example is drawn from the Oregon Youth Study (2 cohorts of 4th grade boys from high crime areas; approx. 200 working class Caucasian families). We were interested in examining the relation between grade 4 maternal discipline tactics (observed inept discipline) in predicting growth in antisocial behavior (TRF externalizing subscale) from grade 4 to grade 8 and the possible moderation of this relation by grade 4 boy anger regulation (mother-reported tantrums). It is quite difficult to detect such interactions in naturalistic field research with representative samples due to measurement error (e.g., low reliability) and range restriction problems. Traditional approaches based on categorizing or dichotomizing continuous moderator variables can worsen the problem by distorting significance levels and effect sizes by attenuating or exaggerating effects. To remedy these problems, high-risk samples can be used to decrease range restriction and latent variable models can be used to decrease measurement error. In addition, growth mixture modeling can be used to reduce cut point selection problems. Often samples will contain qualitatively distinct but latent subpopulations with different means, standard deviations, predictive relations and important differences become lost when distributions are lumped together. Growth mixture modeling can identify the latent subgroups and choose an optimal cut point to create clusters of people who share behavioral characteristics while accounting for statistical uncertainty. Here, the best cut point was at the 80th percentile of tantrum behavior. There was no relationship between maternal discipline and change in externalizing behavior for the low and medium tantrum groups, but there was a strong relationship for the high tantrum group (top 20%). Maternal discipline accounted for no variance in change in TRF scores for the low and medium tantrum groups, but accounted for all of the variance in the high tantrum group (Stoolmiller, 2001).

Michael Stoolmiller's presentation "Using Growth Mixture Models To Study Growth Curves Under Non-standard Conditions: Examples With Synergistic Interactions And Latent Classes" can be viewed in PDF format, using Adobe® Acrobat® Reader®.