UCLA

The UCLA Neurocognitive Family Study (NFS) collected multiple measurements on

schizophrenia (SZ) patients and their relatives, as well as control subjects and their

relatives, to study heritable vulnerability factors for schizophrenia. Each family has

several members enrolled in the study and the same multiple outcomes were measured on each person. The relationship structure is complicated because not only observations on individuals from the same family are correlated, but the multiple outcome measures on the same individuals are also correlated. Traditional familial data analyses model outcomes separately and thus do not provide information about the interrelationships among them. I propose a Bayesian Family Factor Model (BFFM), which extends the classical confirmatory factor analysis (CFA) model to explain the correlations among observed variables using a combination of family-member factors and outcome factors. Traditional methods for fitting CFA models, such as full information maximum likelihood (FIML) estimation using quasi-Newton optimization (QNO) can have convergence problems and Heywood cases caused by empirical under-identification. In contrast, modern Bayesian Markov chain Monte Carlo (MCMC) handles these inference problems easily. Simulations compare the BFFM to FIML-QNO in settings where the true covariance matrix is identified, close to not identified and not identified. For these settings, FIML-QNO fails to fit the data in 85%, 57% and 13% of the cases, respectively, due to non-convergence or invalid estimates, while MCMC provides stable estimates. When both methods successfully fit the data, estimates from the BFFM have smaller variances and comparable mean squared errors. BFFM can test hypotheses of interest easily using Bayes factors computed as the Savage-Dickey ratios. I illustrate the BFFM by analyzing the UCLA NFS data and test hypotheses about differences in means between SZ and control families. Tests of the group mean differences using posterior probabilities suggest that SZ probands perform worse in all 17 neurocogitive measures than control probands, while mothers of SZ subjects do worse than control mothers.