## Decomposing individual and group differences of categorical variables with genetic factor model

##### Abstract

The method of decomposing individual and group differences on ordered categorical variables into genetic and environmental factors is introduced. Although the genetic factor model is used to identify the relative contributions of genetic and environmental factors on individual differences of phenotypic behavior, Dolan (1989) and Dolan, Molenaar, and Boomsma (1992) developed the method to decompose phenotypic means of variables with the genetic and environmental factors. Often, psychological constructs are measured by ordered categorical variables which can restrict the application of genetic factor model. Assuming an ordered categorical variable as a discretization of underlying latent continuous variable, the latent continuous variable can be modeled by applying (LRV) formulation. The present paper proposes a genetic factor decomposition similar to that proposed by Dolan and colleagues but for ordered polytomous variables in which mean structures of phenotype indicators are included. An example of the approach is described using the data from Australian Twin Registry on conservatism scale. Mean differences between men and women are modeled with genetic and environmental factors. Although the patterns of factor loadings and factor means are different for each sub-dimension of conservatism, the model with means fits well to each sub-dimension which indicates that the source of individual and group differences of conservatism measure are similar.

##### Degree

M.A.