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The $L_1$ 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 $L_1$ 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.続きを見る
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