Question 1

What type of evidence is exploratory factor analysis often used to determine?&#10;A) consequential validity&#10;B) construct validity&#10;C) criterion validity&#10;D) reliability

Accepted Answer

What exploratory factor analysis allows us to do is to work with all variables simultaneously, but at the same time know something about their underlying data structure. Exploratory factor analysis is therefore often used to provide evidence of construct validity.

Question 2

Finding which one of the following types of variance is the goal of exploratory factor analysis?&#10;A) common variance&#10;B) error variance&#10;C) specific variance&#10;D) total variance

Accepted Answer

The underlying focus of factor analysis deals with finding common variance (distributed among the factors) and eliminating the unique variance that is not of interest (where total variance = common variance + specific variance + error variance).

Question 3

Exploratory factor analysis is also sometimes known as which one of the following?&#10;A) component factor analysis&#10;B) common factor analysis&#10;C) principal components analysis&#10;D) confirmatory factor analysis

Accepted Answer

Exploratory factor analysis, EFA, is sometimes known as 'common factor analysis.'

Question 4

If your goal is only data reduction, which one of the following should be applied to your data?&#10;A) confirmatory factor analysis&#10;B) exploratory factor analysis&#10;C) principal components analysis&#10;D) structural equation modeling

Accepted Answer

PCA can be used to estimate and understand the contributions of the variables to the linear components within the data, but PCA is simply a method of decomposition-a technique for data reduction only.

Question 5

Which one of the following would be variables with the most appropriate measurement scales for conventional factor analysis?&#10;A) 10 items related to employability that are measured on a three-point Likert scale&#10;B) 10 test items which are each coded as correct or incorrect&#10;C) 15 subscales which are each measured on a scale of 0-25&#10;D) 20 satisfaction items, each coded as yes or no

Accepted Answer

With conventional factor analysis, the computed correlation matrix is a Pearson matrix. This, therefore, suggests that the variables applied must be metric (at least interval in scale) so that a linear relationship exists between the variables.

Question 6

Which one of the following may arise when using binary data in conventional factor analysis?&#10;A) factors are easier to interpret&#10;B) factor solution with too few factors&#10;C) the assumption of linearity will always be met&#10;D) variables with similar splits will correlate even if the context of correlation doesn't make sense

Accepted Answer

Categorical variables that have similar splits will tend to correlate even if the context of correlation of the variables doesn't make sense (see Gorsuch, 1983). This problem is augmented with binary data where correlations tend to reflect similar 'difficulty' as evidenced in a testing type of environment.

Question 7

A researcher wishes to determine the factor structure of 20 continuous items and identify substantive meaning for those factors, for which existing theory for determining the relationships between variables is minimal. Which one of the following procedures is more appropriate?

A) confirmatory factor analysis
B) exploratory factor analysis
C) principal components analysis
D) structural equation modeling

Accepted Answer

EFA is appropriate when the goal is more than just decomposition, i.e., identifying constructs and attaching meaning to them, and when existing theory is minimal.

Question 8

Outlying variables can be determined by which one of the following?&#10;A) critical values for hypothesis test for a single multivariate outlier using Mahalanobis distance&#10;B) largest squared and plot of squared Mahalanobis distance&#10;C) multivariate normality omnibus test&#10;D) weak correlations with the factors that are identified in the factor analytic model

Accepted Answer

Not only are we concerned with outlying cases, but we are also concerned with outlying variables and will need to examine our data for both. These outlying variables, which can be removed from the model if/when identified, can be determined by examination of the following: (a) squared multiple correlations with all other variables and (2) weak correlations with the factors that are identified in the factor analytic model.

Question 9

Which one of the following factor loadings would lead to a recommendation to discard a variable in a factor?&#10;A) 0.1&#10;B) 0.3&#10;C) 0.5&#10;D) 0.8

Accepted Answer

Factor loadings of at least .30 are recommended for retaining a variable in the model.

Question 10

Which one of the following factor loadings would lead to a recommendation to discard a variable in a factor?&#10;A) bivariate scatterplots that suggest a linear relationship between variables&#10;B) R squared values, computed from a regression model for an individual variable where that variable is the dependent variable and all remaining variables are the independent variables, which are near zero&#10;C) statistically significant Mahalanobis distance scores&#10;D) units that have been randomly sampled from a population

Accepted Answer

Multivariate outliers are evidenced by statistically significant Mahalanobis distance scores (alpha = .001 if you tend toward the liberal edge, which is appropriate with EFA), evaluated using a chi square distribution with degrees of freedom equal to the number of variables.

Deck 9: Exploratory Factor Analysis