Page 80 - The value of total hip and knee arthroplasties for patients

Chapter 5
Assessing factorial invariance involves a process of comparing the fit indices for a series of models with increasingly stringent constraints on the relationships between the model parameters.The best-fitting model for the total sample (TKA andTHA) identified in the previous analysis was assessed in multigroup CFA’s to test for factorial invariance across theTKA andTHA groups.28 Four multigroup CFA models with increasingly stringent model constraints were tested (Table 1):
• A baseline model (configural invariance): in which only the factor structure (number of factors and the pattern of the free and fixed loadings) was constrained to be equal across groups. In this model no equality constraints were imposed on the intercepts and factor loadings.
• A weak FI model: in which the factor structure and factor loadings were constrained to be equal across groups, intercepts were allowed to vary among groups and factor variances were fixed to one in both groups.
• A strong FI model: in which factor structure and loadings and intercepts (thresholds) were constrained to be equal across groups.
• A strict FI model: in which factor structure, factor loadings, intercepts and residual variances were constrained to be equal across groups.
To evaluate the degree of measurement invariance, the recommendations by Cheung and Rensvold38 were followed, which state that the null hypothesis (invariance) is kept if the incremental change in comparative fit index (CFI) is equal to or smaller than 0.01.9 Acceptance of the strong or the strict invariance model was sufficient to assume that the measurement instruments used measure the same constructs in all participants (bothTHA andTKA).
Missing data were incorporated by using the default option available in Mplus. For WLMSV estimation, Mplus computes polychoric correlations based on pairwise present data between two variables, treating missing data as missing completely at random (MCAR). Under MCAR, the missingness is assumed to occur entirely at random and not depend on observed covariates or on the response itself.
Table 1: levels of factorial invariance
FI Models
No FI Weak FI Strong FI Strict FI
Model parameters constrained to be equal across groups
None
Factor loadings
Factor loadings and item intercepts (thresholds)
Factor loadings and item intercepts (thresholds) and residual item variances/covariances
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