Measurement Bias Detection Through Factor Analysis

Abstract

Measurement bias is defined as a violation of measurement invariance, which can be investigated through multigroup factor analysis (MGFA), by testing across-group differences in intercepts (uniform bias) and factor loadings (nonuniform bias). Restricted factor analysis (RFA) can also be used to detect measurement bias. To also enable nonuniform bias detection, we extend RFA with latent moderated structures (LMS) or use a random slope parameterization (RSP). In a simulation study we compare the MGFA, RFA/LMS, and RFA/RSP methods in detecting measurement bias, varying type of bias (uniform, nonuniform), type of the variable that violates measurement invariance (dichotomous, continuous), and its relationship with the trait that we want to measure (independent, dependent). For each condition, 500 sets of data are generated and analyzed with each of the three detection methods, in single run and in an iterative procedure. The RFA methods outperform MGFA when the violating variable is continuous.

Keywords:

• factor analysis
• latent moderated structures
• measurement invariance
• nonuniform measurement bias
• random slope parameterization

Notes

See Equation 2: ^a u = 0, mean(T) = mean(V) = mean(E) = 0, var(T) = var(V) = var(E) = 1.

^bvar(T) ₁ = var(T) ₂ = 1, mean(E) ₁ = mean(E) ₂ = 0, var(E) ₁ = var(E) ₂ = 1.

^aMeans, standard deviations, and proportions are calculated over 500 observations.

^bMeans, standard deviations, and proportions are calculated over 500 × 6 = 3,000 observations in Conditions 1, 5, 9, and 13, and over 500 × 5 = 2,500 observations in all other conditions.

^aProportions are calculated over 500 observations.

^bProportions are calculated over 500 × 6 = 3,000 observations in Conditions 1, 5, 9, and 13, and over 500 × 5 = 2,500 observations in all other conditions.

^aMeans, standard deviations, and proportions are calculated over 500 observations.

^bMeans, standard deviations, and proportions are calculated over 500 × 6 = 3,000 observations in Conditions 1, 5, 9, and 13, and over 500 × 5 = 2,500 observations in all other conditions.

^cAfter removal of 2, 1, and 2 outliers in Conditions 3, 7, and 8; before removing outliers, means (M) and standard deviations (SD) are M = 18.559 and SD = 16.506 in Condition 3, M = 25.740 and SD = 26.262 in Condition 7, and M = 42.599 and SD = 66.751 in Condition 8.

^aMeans, standard deviations, and proportions are calculated over 500 observations.

^bMeans, standard deviations, and proportions are calculated over 500 × 6 = 3,000 observations in Conditions 1, 5, 9, and 13, and over 500 × 5 = 2,500 observations in all other conditions.

^cAfter removal of 2, 2, and 3 outliers in Conditions 3, 7, and 8; before removing outliers, means (M) and standard deviations (SD) are M = 18.518 and SD = 16.399 in Condition 3, M = 25.618 and SD = 25.245 in Condition 7, and M = 42.481 and SD = 65.462 in Condition 8.

^aProportions are calculated over 500 observations.

^bProportions are calculated over 500 × 6 = 3,000 observations in Conditions 1, 5, 9, and 13, and over 500 × 5 = 2,500 observations in all other conditions.