Daniel McNeish said Exploratory factor analysis (EFA) is an extremely popular method for determining the underlying factor structure for a set of variables. Due to its exploratory nature, EFA is notorious for being conducted with small sample sizes, and recent reviews of psychological research have reported that between 40% and 60% of applied studies have 200 or fewer observations. Recent methodological studies have addressed small size requirements for EFA models; however, these models have only considered complete data, which are the exception rather than the rule in psychology. Furthermore, the extant literature on missing data techniques with small samples is scant, and nearly all existing studies focus on topics that are not of primary interest to EFA models. Therefore, this article presents a simulation to assess the performance of various missing data techniques for EFA models with both small samples and missing data. Results show that deletion methods do not extract the proper number of factors and estimate the factor loadings with severe bias, even when data are missing completely at random. Predictive mean matching is the best method overall when considering extracting the correct number of factors and estimating factor loadings without bias, although 2-stage estimation was a close second.

1. Exploratory Factor Analysis With
Small Samples and Missing Data
Daniel McNeish
Presented by: Fatemeh Nikbakht

2. Outline
● Exploratory Factor Analysis
● What’s problem?
● Overview of common missing data techniques
● Small sample issues for each method
● Simulation study
● Discussion
● Limitations
● Your review
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3. Exploratory Factor Analysis
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4. What’s problem?
● EFA notorious for being conducted with small
sample sizes.
● psychological research 200 or fewer observations.
● Recent methodological studies considered complete data
exploratory nature
between 40% and 60%
comparative small sample missing data uninformative
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5. What’s problem?
● missing data and EFA (irrelevant or secondary)
● Exploratory aim of EFA, small sample missing data the literature are
largely uninformative
● modern techniques (maximum likelihood and multiple
imputation) converge with large samples, diverge with smaller
samples
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6. Overview of common missing data techniques
Two-stage estimation
● Fully direct ML
● NOTE direct ML simultaneously accounts for
missing values and estimation of model
parameters at each iteration.
first stage
stimate of the correlation
matrix that accounts for
the missing values
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second stage
stage does not
necessarily have to be
estimated with ML

7. Overview of common missing data techniques
Multiple imputation with fully conditional specification
● Imputation ,Analysis ,Pooling
● many different ways to create
imputed values : two common
methods fully conditional
specification imputation (FCS)
○ FCS-R
○ FCS-predictive mean
matching (PMM)
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8. Small sample issues for each method
1) Listwise and pairwise deletion
2) Two-stage estimation
3) FCS imputation
a) FCS-PMM
b) FCS-R
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9. Simulation study
● Design and data generation
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10. Simulation study
● Manipulated conditions and rationales
○ sample size (60, 120, 240)
○ The percent of missing data (5%, 10%, 25%)
○ The missing data technique (TSE, PMM, FCS–R, LD, PD)
○ Type of missing mechanism (MAR, MCAR)
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11. Discussion
1) Sample sizes grow large ⇒ results improve
2) Missing data grow large ⇒ result is worse
3) Deletion methods ⇒ worst choice to handle missing data ( commonly
known (unbiased with MCAR data))
4) PMM (preferred method) ⇒ proper number of factors & lowest bias
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12. Limitations
1) Maybe data manipulation is not possible
2) Data generation model (clean)
3) ...
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13. Your review
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Positive
● Investigate different methods
● Fuger & tabales
● History of studies related to sample
data size
Negative
● Scientific article (results)
● Explain exploratory factor analysis
● Very specialized
● Ambiguity in the data

14. Thank You for Your
Attention:)
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