The paper addresses the issue of measurement invariance in the analysis of preventive intervention data. Procedures for testing the invariance of covariance matrices, measurement models, and structural growth models are illustrated using data from an early intervention program for low birth weight, preterm infants. Intelligence Quotient (IQ) measured at 5 time points was modeled using piecewise growth curve analysis. Change over time in children's cognitive development was modeled separately for the pre- and postintervention periods. The first period was during the intervention, which lasted from birth through age 3 years. The second was during the postintervention period, which included follow-up assessments at ages 5 and 8 years. The analytical approach is illustrated with findings indicating that the development of IQ was different for higher low birth weight (HLBW: 2001-2500 g) and lower low birth weight (LLBW: <2001 g) infants. Examination of the effects of covariates on the IQ trajectories associated with the two birth weight groups indicated differential effects on IQ depending on the period of development and birth weight. Neonatal health and maternal age were predictors of IQ change in the LLBW group whereas maternal education was related to change in the HLBW group. During the posttreatment period, only Hispanic ethnicity and treatment group status were related to change. Hispanic participants exhibited an accelerated trajectory between program end and age 8 years. Intervention recipients exhibited a flatter trajectory during the same time period whereas participants in the control group exhibited an accelerated development, essentially catching up with their counterparts in the treatment group. Results clearly illustrate the utility of invariance testing in modeling developmental trajectories in response to preventive intervention.