Partial F‐tests with multiply imputed data in the linear regression framework via coefficient of determination

Tests for regression coefficients such as global, local, and partial F-tests are common in applied research. In the framework of multiple imputation, there are several papers addressing tests for regression coefficients. However, for simultaneous hypothesis testing, the existing methods are computationally intensive because they involve calculation with vectors and (inversion of) matrices. In this paper, we propose a simple method based on the scalar entity, coefficient of determination, to perform (global, local, and partial) F-tests with multiply imputed data. The proposed method is evaluated using simulated data and applied to suicide prevention data.

[1]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[2]  M. Polen,et al.  Behavioral Counseling Interventions in Primary Care To Reduce Risky/Harmful Alcohol Use by Adults: A Summary of the Evidence for the U.S. Preventive Services Task Force , 2004, Annals of Internal Medicine.

[3]  J. Schafer,et al.  Missing data: our view of the state of the art. , 2002, Psychological methods.

[4]  Jerome P. Reiter,et al.  Small-sample degrees of freedom for multi-component significance tests with multiple imputation for missing data , 2007 .

[5]  J. Graham,et al.  How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory , 2007, Prevention Science.

[6]  D. Rubin,et al.  Small-sample degrees of freedom with multiple imputation , 1999 .

[7]  Ofer Harel,et al.  The estimation of R 2 and adjusted R 2 in incomplete data sets using multiple imputation , 2009 .

[8]  Paul T. von Hippel,et al.  TEACHER'S CORNER: How Many Imputations Are Needed? A Comment on Hershberger and Fisher (2003) , 2005 .

[9]  Donald B. Rubin,et al.  Performing likelihood ratio tests with multiply-imputed data sets , 1992 .

[10]  Ofer Harel,et al.  Inferences on missing information under multiple imputation and two-stage multiple imputation , 2007 .

[11]  R. Aseltine,et al.  An outcome evaluation of the SOS Suicide Prevention Program. , 2004, American journal of public health.

[12]  Todd E. Bodner,et al.  What Improves with Increased Missing Data Imputations? , 2008 .

[13]  D. Rubin.  Multiple Imputation After 18+ Years , 1996 .

[14]  J. McAlaney,et al.  Change over time in alcohol consumption in control groups in brief intervention studies: systematic review and meta-regression study. , 2009, Drug and alcohol dependence.

[15]  D. Rubin,et al.  Large-sample significance levels from multiply imputed data using moment-based statistics and an F reference distribution , 1991 .

[16]  J. Schafer,et al.  A comparison of inclusive and restrictive strategies in modern missing data procedures. , 2001, Psychological methods.

[17]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .