Outliers and Linearity for EFA

Question

I am having 56 likert scaled items for IV and 28 likert scaled items for dv. As to fulfill the assumption for EFA, outliers and linearity need to be checked. Can anyone tells me what method/analysis is the best for identifying outliers and linearity? For outliers, can I use Z-scores?

Answer 1

EFA is closely related with principal components analysis (PCA), so some observations about outlier detection in that setting may be relevant to you. Indeed, it is possible to perform a form of factor analysis using PCA

One way to quantify outlyingness in PCA is a measure called the orthogonal distance, which is the distanceof the observations to the PCA subspace. This is defined as

$\mbox{OD}(\pmb x_i,\pmb t^*,\pmb P_q^*)=||\pmb x_i-\pmb t^*-(\pmb x_i-\pmb t^*)\pmb P_q^*(\pmb P_q^*)'||$,

where here $\pmb t^*$ is the estimated center, and \pmb P_q^* are the first $q$ most important of the estimated PCA loadings. A number of robust PCA methods output these distances. For examples, see:

ROBPCA: This can be performed using the PcaHubert function in the R package rrcov, or in Matlab with the LIBRA toolbox. Using R, if you fit a ROBPCA model, you can type plot(model) and you will get an outlier plot

FastHCS: This method is implemented for R as FastHCS. You can produce an outlier plot for this method by training model and then executing the following code:

plot(model\$rew.fit\$sd, model\$rew.fit\$od)

abline(h = model\$rew.fit\$cutoff.od )

abline(v = model\$rew.fit\$cutoff.sd )

The papers corresponding to both of the robust PCA methods provide some insight into how to interpret the outlier detection results. These outliers should likely also be important outliers for EFA.