On the surface, it seems there is no reason not to report effect sizes and their corresponding confidence intervals. In the BESS, a large debate has been underway for some time about the importance of re- porting effect sizes and confidence intervals (e.g., Schmidt 1996 Meehl 1997 Thompson 2002 Cohen 1994 Kline 2004, and the references contained therein) rather than only the dichoto- mous reject or fail-to-reject decision from a null hypothesis significance test (see Krantz 1999, for a review of the tension that sometimes exists between statisticians and methodologists regarding this debate). As far as we know, many algorithms performing PCA with missing values do not include these re-centering or re-scaling steps and thus variables do not have the same weights in the analysis. In the incomplete case, it is necessary to consider the scaling process as a part of the analysis. In the complete case, scaling is often carried out prior to analysis and thus often regarded as a pre-processing step.

In the same vein, if one wishes to perform a standardized PCA (to give the same weight to each variable in the analysis) with missing values, a rescaling step must be incorporated after each imputation step. Consequently, it is necessary to recenter the data after each imputation step.

Indeed, after each imputation step, the means of the variables change. First, note that the mean matrix M is updated during the algorithm. Much can be said about the regularized iterative PCA algorithm. Ij в€’ Л† x ` ij ) 2 в‰¤ Оµ, with Оµ equal to 10ДЄdditional justification for the specific regularization shown here is given in Verbanck, Josse, and Husson ( 2013 ).

Xlstat statistical