Research Seminar
Principal Covariates Regression: How to weigh and rotateMarlies VervloetKU Leuven | |
| Abstract: | As is commonly known, ordinary linear regression falls short when the predictor variables are highly correlated with each other, because in that case the estimates of the regression weights tend to be unstable. Principal Covariates Regression (PCovR) was developed by De Jong & Kiers (1991) as a solution to this problem. PCovR combines the main ideas behind Principal Component Analysis (PCA) and regression. Like PCA, PCovR reduces the variables to a few components and, like regression, it predicts the criterion variables, but using the components as predictor variables. Specifically, PCovR minimizes the following criterion: α |X – TPx|² ˖ (1 - α) |Y-TPy|², where X and Y are the scores on, respectively, the predictor and the criterion variables, α is the weighing parameter, which indicates the extent to which the reconstruction of the predictor scores and the criterion scores are emphasized, T contains the scores of the observations on the components, Px includes the loadings of the predictor variables on the components, and Py are the regression weights of the components when predicting the criterion variables. Although PCovR is potentially a very interesting method (e.g., there are strong relations with exploratory SEM; Asparouhov & Muthén, 2009), it is rarely used. This might be because the estimates of the regression weights Py display rotational freedom. Another issue is the optimal value of the weighing parameter α. In this paper, based on extensive simulations, we make some recommendations on how to deal with the rotational freedom and the selection of the value of α. |
| Date: | Tue Apr 26, 12:15 pm - 1:15 pm |
| Place: | room 02.60 (Department of Psychology, Tiensestraat 102, 3000 Leuven) |