Genetic Tobit factor analysis: quantitative genetic modeling with censored data

Parameters of quantitative genetic models have traditionally been estimated by either algebraic manipulation of familial correlations (or familial mean squares), biometric model fitting, or multiple-group covariance structure analysis. With few exceptions, researchers who have used these methods for the analysis of twin data have assumed that their data were multinormal and, consequently, have used normal-theory estimation methods. It is shown that normal-theory methods produce biased genetic and environmental parameter estimates when data are censored. Specifically, with censored data, (1) normal-theory estimates of narrow-sense heritability are either positively or negatively biased, whereas (2) estimates of shared-familial environmental variance are always biased downward. An alternative method for estimating genetic and environmental parameters from censored twin data is proposed. The method is called genetic Tobit factor analysis (GTFA) and is an extension of the Tobit factor analysis model developed by Muthén (Br. J. Math. Stat. Psychol. 42, 241-250, 1989). Using a Monte Carlo design, the performance of GTFA is compared to traditional quantitative genetic methods in both large and small data sets. The results of this study suggest that GTFA is the preferred method for the genetic modeling of censored data obtained from twins.