Variable selection via the grouped weighted lasso for factor analysis models
نویسندگان
چکیده
The L1 regularization such as the lasso has been widely used in regression analysis since it tends to produce some coefficients that are exactly zero, which leads to variable selection. We consider the problem of variable selection for factor analysis models via the L1 regularization procedure. In order to select variables each of which is controlled by multiple parameters, we treat parameters as grouped parameters and then apply the grouped lasso. Crucial issues in this modeling procedure include the selection of the number of factors and regularization parameters. Choosing these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for evaluating a factor analysis model via the grouped lasso. The proposed procedure produces estimates that lead to variable selection and also selects the number of factors objectively. Monte Carlo simulations are conducted to investigate the effectiveness of the proposed procedure. A real data example is also given to illustrate our procedure.
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