, Volume 66, Issue 4, pp 563-575

First online:

Regression among factor scores

  • Anders SkrondalAffiliated withDepartment of Epidemiology, National Institute of Public Health Email author 
  • , Petter LaakeAffiliated withSection of Medical Statistics, University of Oslo

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.

Key words

regression factor scores structural equation models latent variables factor score regression