Regression among factor scores

By A. Skrondal, Petter Laake. 2001

458 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Food Science, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/cc78e2ea3bb24aedf26f01256af175a3619818cf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Food Science

In Management Science and Operations Research

Citations in the corpus

Information Technology Competencies, Organizational Agility, and Firm Performance: Enabling and Facilitating Roles (2013, methodology): “Following recommendations from Skrondal and Laake (2001) we use blockwise factor scores—speciﬁcally, regression factor scores for independent latent constructs and Bartlett factor scores for the dependent latent construct—then apply them in the CLCRA estimation.”
Motivation profiles at work: A self-determination theory approach (2016, unknown): “In comparison with scale scores, factor scores have the advantage of providing a partial control for measurement errors by giving more weight to items presenting lower levels of measurement errors (Kam et al., 2016; Morin & Marsh, 2015; Skrondal & Laake, 2001).”
Benefiting from economic crisis? Strategic orientation effects, trade-offs, and configurations with resource availability on SME performance (2020, methodology): “To produce consistent estimators for all parameters, regression factor scores for the explanatory latent variables along with a Bartlett score for the latent response variable were used (Skrondal and Laake 2001).”
Examining the Relations Between Executive Function, Math, and Literacy During the Transition to Kindergarten: A Multi-Analytic Approach (2017, methodology): “The use of factor scores as dependent variables is known to produce biased regression slopes and standard errors (Muthén, 2011; Skrondal & Laake, 2001).”
Perceptions of HR practices, person–organisation fit, and affective commitment: The moderating role of career stage (2018, methodology): “Considering the proportion of the number of items measuring our core concepts, alongside the number of participants, we followed recommendations of Skrondal and Laake (2001) and included Bartlett factor scores of the bundle of perceived HPWP, PO fit and affective commitment in our model.”
Small Sample Size Solutions (2020, methodology): “If used naïvely, factor score regression will likely lead to substantial bias in the estimated parameters of the structural part, even when the sample size is very large (Skrondal & Laake, 2001), because the factor scores have been treated as if they were observed without measurement error.”
Classroom Climate and Contextual Effects: Conceptual and Methodological Issues in the Evaluation of Group-Level Effects (2012, background): “(2009; Ludtke et al, 2011 ; Ludtke et al, 2008 ; also see Skrondal & Laake, 2001 ) 2 argued that the “best” estimate of the contextual effect typically lies somewhere between the doubly latent model (that might overcorrect for sampling error, leading to inflated estimates of the contextual e”
Emotional labour profiles: Associations with key predictors and outcomes (2018, methodology): “…errors the way latent variables do, however they provide a partial control for measurement errors by giving more weight to more reliable items (Skrondal & Laake, 2001), and preserve the underlying nature of the measurement model (e.g. measurement invariance) better than scale scores (Morin et…”
Evidence of a continuum structure of academic self-determination: A two-study test using a bifactor-ESEM representation of academic motivation (2017, methodology): “Still, in order to achieve at least a partial level of correction for measurement errors (e.g., Skrondal & Laake, 2001; Morin, Meyer, Creusier, & Biétry, 2016), these outcomes were represented by factors scores saved from a preliminary measurement models (Vitality: χ2 = 13.989, df = 14, p > .05;…”
Multiple-Group Analysis of Similarity in Latent Profile Solutions (2016, methodology): “Key to the realization of systematic quantitative comparisons of the results obtained across meaningful subgroups of employees is the availability of a proper methodological and statistical approach to guide these comparisons (e.g., Riordan & Vandenberg, 1994; Spector et al., 2015).”