Longitudinal patterns of financial product ownership: a latent growth mixture approach

Latent growth models consider both intra-individual change and inter-individual differences in such change by estimating the amount of variation across individuals in the latent growth factors (random intercepts and slopes) as well as the average growth (Kreuter and Muthén, 2008). The assumption of homogeneity in the growth parameters – same parameters for all individuals – does not always correspond to the reality. If heterogeneity exists and is ignored, statistical results can be seriously biased. Mixture modeling aims to unmix the population into an unknown number of latent classes or subpopulations (Duncan et al., 2002). Thus, latent growth mixture modeling (LGMM) allows that the population of interest is not homogeneous, but consisting of subpopulations with varying parameters and within-class variation (Muthén, 2006). This paper illustrates the enormous potential of this type of longitudinal latent variable modeling that combines discrete and continuous latent variables. The application estimates the evolution of financial products ownership at household level in Italy in the period 2000 to 2008. We model the binary indicators of ownership (e.g., household owns bonds) as multiple indicators of a latent process that can differ at segment level. Covariates can directly model the probability of each household belongs to a given segment.