Non-normal path analysis in the presence of measurement error and missing data: a Bayesian analysis of nursing homes' structure and outcomes

Abstract

Path analytic models are useful tools in quantitative nursing research. They allow researchers to hypothesize causal inferential paths and test the significance of these paths both directly and indirectly through a mediating variable. A standard statistical method in the path analysis literature is to treat the variables as having a normal distribution and to estimate paths using several least squares regression equations. The parameters corresponding to the direct paths have point and interval estimates based on normal distribution theory. Indirect paths are a product of the direct path from the independent variable to the mediating variable and the direct path of the mediating variable to the dependent variable. However, in the case of non-normal distributions, the point and interval estimates of the indirect path become much more difficult to estimate. We address the issue of calculating indirect point and interval estimates in the case of non-normally distributed data. Our substantive application is a nursing home research problem in which the variables in the path analysis of interest involve variables with normal, Bernoulli, or Poisson distributions. Additionally, one of the Poisson variables is observed with error. This paper addresses estimating point and interval estimation of indirect paths for variables with non-normal distributions in the presence of missing data and measurement error. We handle these difficulties from a fully Bayesian point of view. We present our substantive path analysis motivated from a nursing home structure, process, and outcomes model. Our results focus on the impact job turnover in the nursing homes has on nursing home outcomes.