Structural equation models and small sample bias reduction with application to fishery data

Abstract

An overview of structural equation models is presented along with an application to fishery data involving estimation and significance testing of the density dependent component of recruitment in 6 cod populations. Estimates and standard errors are based on normal theory and large sample properties of maximum likelihood estimates. The data sets analyzed involve small sample sizes so a sensitivity analysis of the effect (in terms of bias) of small sample sizes and other deviations in model assumptions is conducted. The analysis indicates that sample size is the most influential factor considered on the bias of parameter estimates. The reliability of indicator variables is also important. – Two methods of reducing the bias in estimates are considered, they are the jackknife and a method based on a Taylor’s series expansion of the log likelihood function. The bias reduced estimators are investigated by simulating several confirmatory factor models. Neither the Jackknife nor the Taylor’s series biased reduced estimator works sufficiently well to warrant their application in practice. Both estimators consistently reduce bias in the maximum likelihood estimates only when little bias exists. A difficulty realized in the investigation is that the expectations of some estimators are unbounded and this makes bias reduction difficult.