Investigating weight constraint methods for causal-formative indicator modeling

Causal-formative indicators are often used in social science research. To achieve identification in causal-formative indicator modeling, constraints need to be applied. A conventional method is to constrain the weight of a formative indicator to be 1. The selection of which indicator to have the fixed weight, however, may influence statistical inferences of the structural path coefficients from the causal-formative construct to outcomes. Another conventional method is to use equal weights (e.g., 1) and assumes that all indicators equally contribute to the latent construct, which can be a strong assumption. To address the limitations of the conventional methods, we proposed an alternative constraint method, in which the sum of the weights is constrained to be a constant. We analytically studied the relations and interpretations of structural path coefficients from the constraint methods, and the results showed that the proposed method yields better interpretations of path coefficients. Simulation studies were conducted to compare the performance of the weight constraint methods in causal-formative indicator modeling with one or two outcomes. Results showed that higher biases in the path coefficient estimates were observed from the conventional methods compared to the proposed method. The proposed method had ignorable bias and satisfactory coverage rates in the studied conditions. This study emphasizes the importance of using an appropriate weight constraint method in causal-formative indicator modeling.