Scale Creation and Exploratory Factor Analysis

Question 1

Explain the three different construct dimensionalities

Answer 1

Latent model underlining construct which cannot be measured, ex. Organizational attractiveness. Instead, it is to be measured on its dimensions.
o Constructs can be measured on the same scale.
o Expect subdimensions to be correlated and therefore reflect the underlying construct together.
o Want to measure what the dimensions have in common
o Usually scales.

Aggregate model: the multidimensional constructs can be formed as an algebraic function of its dimensions.
o add dimensions together to understand the construct.
o Usually indexes
o The constructs is formed from its dimensions.

Profile model: the multidimensional constructs is interpreted as various profiles formed by pairing the characteristics of different dimensions.
o combine subdimensions to understand the construct, ex. Personality.
o Specific different levels of dimensions and interpret the construct by profiling the levels.
o Don’t look at it as an average or added up together.

Question 2

Define different types Variances of the Construct

Answer 2

Observed variances of a variable can be partitioned into four elements:
o Common variances: those shared by all dimensions of the multidimensional construct.
o Group variances: those shared by only some dimensions.
o Specific variances: variances unique to a single dimension.
o Random variances: variances caused by random factors

Question 3

What are seen as true variances under the latent model?

Answer 3

• Under the latent model, only common variances and covariances shared by all dimensions are seen as true variances of the construct.
  o The other type of variance is seen as error variances.

Question 4

What are seen as true variances under the aggregate model?

Answer 4

Under the aggregate model, all but random variance, are seen as true variances, while random variance is seen as error variances.

Question 5

What are seen as true variances under the profil model?

Answer 5

Under the profile model, depending on the dichotomization criterion, the proportion that is considered as true variances may or may not cover the common variances, group variances, or specific variances.

Question 6

In EFA how many measured variables are recommended to represent one factor?

Answer 6

At least three to five measured variables representing each common factor should be included

Question 7

When should EFA be used?

Answer 7

EFA should be used when the primary goal is to identify latent constructs and there is insufficient basis to specify a prior model.
associated with theory development

Question 8

When should CFA be used?

Answer 8

CFA should be used when the goal is to identify latent constructs and a substantial basis exist to specify a prior model.
associated with theory testing.

Question 9

When should principal component analysis be used?

Answer 9

If the goal is data reduction, principal components analysis is more appropriate.

Question 10

When selecting the number of factors in EFA what is the trade-off?

Answer 10

Balance the need for parsimony (i.e., a model with relatively few common factors) against the need for plausibility (i.e., a model with sufficient number of common factors to adequately account for the correlations among measured variables)
- In general, too few factors are the biggest issue

Question 11

Is overfactoring good?

Answer 11

Yes. Overfactoring often result in rotated solutions in which the major factors are accurately represented, and the additional factors have no measured variables that load substantially on them or have only a single measured variable that loads substantially on each additional factor.

Question 12

What is the Kaiser criterion used for?

Answer 12

computing the eigenvalues for the correlation matrix to determine how many of these eigenvalues are greater than 1.
o This number is used as the number of factors. Retain factors with eigenvalue greater than 1.

Factors should explain at least 60 %

Question 13

What is the Scree test used for?

Answer 13

the eigenvalues of the correlation matrix are computed and then plotted in order of descending values.
o This graph is then examined to identify the last substantial drop in the magnitude of the eigenvalues.

Question 14

Does an EFA model with more than one factor have a unique solution?

Answer 14

An EFA model with more than one factor do not have a unique solution. For any given solution with two or more factors there exists an infinite number of alternative orientations of the factors in multidimensional space that will explain the data equally well.
Hence, why factor rotation is used.

Question 15

What is the general recommendation in terms of rotation i EFA?

Answer 15

oblique rotation

Question 16

What is factor analysis (FA)?

Answer 16

A statistical technique applied to a single set of variables when the researcher is interested in discovering which variables in the set form coherent subsets that are relatively independent of one another.
Variables that are correlated with one another but largely independent of other subsets of variables are combined into factors.

Question 17

Mention the steps in PCA or FA.

Answer 17

Steps in PCA or FA include selecting and measuring a set of variables, preparing the correlation matrix (to perform either PCA or FA), extracting a set of factors from the correlation matrix, determining the number of factors, (probably) rotating the factors to increase interpretability, and, finally, interpreting the results.

Question 18

Explain the two general classes of rotation.

Answer 18

If rotation is orthogonal (so that all the factors are uncorrelated with each other), a loading matrix is produced.
The sizes of the loadings reflect the extent of relationship between each observed variable and each factor.
Orthogonal FA is interpreted from the loading matrix by looking at which observed variables correlate with each factor.
often use varimax rotation.

If rotation is oblique (so that the factors themselves are correlated), several additional matrices are produced. o Choose if we believe that factors are correlated with each other.
Use the pattern matrix, which is representing the “clean” amount of unique variation that the factor explains for each variable.
often use Oblimin rotation.

Question 19

What could be a problem in FA?

Answer 19

Sensitivity to outlying cases, too small sample size, problems created by missing data, and degradation of correlations between poorly distributed variables (must be normally distributed).

singularity or extreme multicollinearity is also a problem.

Question 20

When is normal distribution in FA not as important?

Answer 20

As long as FA is used descriptively as convenient ways to summarize the relationships in a large set of observed variables, assumptions regarding the distributions of variables are not in force.

Question 21

What is rotation used for?

Answer 21

Rotation is ordinarily used after extraction to maximize high correlations between factors and variables and minimize low ones.

Question 22

What is the communality?

Answer 22

The communality for a variable is the variance accounted for by the factors.

Question 23

How can you check for normality in FA?

Answer 23

Values of skewness and kurtosis should be close 0 (+/- 2)

Question 24

How do you check the Factorability of R?

Answer 24

Check correlation matrix for correlations higher than 0,3.

Question 25

Should partial correlation be higher or lower than correlation of items?

Answer 25

Want partial correlation to be lower than correlation because it indicates chains of correlation which can form factors.