# Impact on exploratory factor analysis of limiting number of data imputations

I intend to use multiple imputation to deal with missing continuous data before conducting exploratory factor analysis (EFA) on survey data, and to obtain factor scores for each individual case. I would ideally like to be able to subject the factor scores to further analyses (regression and possibly latent profile analysis).

Background:

• I am a researcher in psychology, and am new to both EFA and data imputation.
• Data: 221 participants answered 60 questions, all of which asked them to indicate the extent of their agreement with a statement on a scale of 0-100.
• During EFA I encounter some very low communalities (below .2). My understanding is that I therefore need to run the analysis multiple times, removing the variable with the lowest communality each time before re-running. On dry runs with singly imputed data, this means I end up with about 25 variables in the final factor solution.
• 95% of the original 60 variables have missing data, which results from selection of a ‘don’t know’ option. The proportion of missing data ranges from 0-10.9% on each variable, with a mean of 3.4%. The missing data are MAR or MCAR, multivariate and non-monotone.
• Most of the variables have data that are skewed, some highly, and some with a high mass near 0 or 100. I want to impute data and conduct EFA in a way that is appropriate for the distribution of the data and results in a minimum of distortion to standard errors.
• I am planning to use the programme FACTOR. It uses hot-deck imputation, which seems to be appropriate for non-normal data, then performs multiple EFAs and averages their factor solutions after Procrustes rotation. Factor scores are simply averaged as well (Lorenzo-Seva & Van Ginkel, 2016; Ferrando & Lorenzo-Seva, 2017). For the EFA I will use Unweighted Least Squares/Principal Axis Factoring to deal with the non-normal distribution, and direct oblimin rotation to obtain an oblique solution.

However, FACTOR limits users to 5 imputations. 95% of my variables have missing data. Bodner (2008) recommends having as many imputations as the percentage of cases with missing data, and Graham (2007) recommends about 100 imputations when 90% or more variables have missing information.

How serious a problem is this limited number of data imputations:

• for the factor solution
• for subsequent parametric analysis using the resulting factor scores?

I have tried an alternative technique that I hoped would avoid this problem: R package mifa calls package mice to impute data – with no limit on the number of imputations - using predictive mean matching (PMM), and combines the resulting covariance or correlation matrices. An averaged covariance or correlation matrix can be passed to package psych for EFA. However, I can only get factor weights this way, not individual factor scores. I assume this is because package psych is using the correlation matrix rather than case-level data. The author of package mifa has been extremely helpful, but mifa cannot currently get to a single set of factor scores for individuals using Rubin’s rules.

## 1 Answer

I have now found Van Buuren's Flexible Imputation of Missing Data (2018). Section 2.8 explains that in cases such as mine, where there is a large number of variables, it may not after all make sense to use the percentage of complete cases to guide the number of imputations. Instead, we can consider using the average missing data rate as a less conservative estimate. For me this is 3.4%, meaning that 5 imputations are, at least on this reasoning, adequate.