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Exploratory Factor Analysis

Q: Intercollinearity test assumptions on correlation FA!

* Sufficient amount of correlation (r>0.3) * Anti-image correlation matrix (with (negative) partial correlations & all partial correlations are small |ρij | < 0.7) * Barlett's test of sphericity test is significant, chi-square value =, p-value = * Measure of Sampling Adequacy overall Kaiser-Meyer-Olkin MSA= > 0.5 variable specific MSA's: all above 0.5

Q: Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy (MSA)

The KMO statistic measures how data are likely to 'factor well' based on correlation and partial correlation. It suggests if the data may be grouped into a smaller set of underlying factors. It varies from 0 to 1 Partial correlation = 0.0 -> common factor -> MSA = 1 Partial correlation = 1.0 -> NO common factor -> MSA = 0 <0.5 unacceptable (no common factor)

Q: Assess the communalities of all variables

* look at communalities tables * treshold > 0.5 ?? * then, all variables have sufficient communality values. * if not: insufficiently explained by factor solution, the variable is omitted

17 important questions on Exploratory Factor Analysis

Difference between PCA and PFA

* PCA is used to reduce the dimensionality of data.

* The total variance is redistributed in p observed variables over p principal components.

* The first principal component has largest

contribution to total variance. The second has the second largest contribution, etc

* PFA is used to summarize/explain the data.

* The method reproduces observed correlations as good as possible, using small number of common factors (m<<p).

* The observed relations between the variables are describing underlying constructs (i.e. the common factors), which may serve further as theoretical deepening.

Intercollinearity test assumptions on correlation FA!

* Sufficient amount of correlation (r>0.3)

* Anti-image correlation matrix (with (negative) partial correlations & all partial correlations are small |ρij | < 0.7)

* Barlett's test of sphericity
test is significant, chi-square value =, p-value =

* Measure of Sampling Adequacy

overall Kaiser-Meyer-Olkin MSA= > 0.5
variable specific MSA's: all above 0.5

Bartlett’s test of sphericity

It compares the correlation matrix to an identity matrix

H0) correlation matrix is the identity matrix

HA) correlation matrix is not the identity matrix

(You reject H0 and conclude that the strength of the relationship among the variables are strong and appropriate for factor analysis )

Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy
(MSA)

The KMO statistic measures how data are likely to "factor well" based on correlation and partial correlation. It suggests if the data may be grouped into a smaller set of underlying factors. It varies from 0 to 1

Partial correlation = 0.0 -> common factor -> MSA = 1

Partial correlation = 1.0 -> NO common factor -> MSA = 0

<0.5 unacceptable (no common factor)

Assess the communalities of all variables

* look at communalities tables

* treshold > 0.5 ??

* then, all variables have sufficient communality values.

* if not: insufficiently explained by factor solution, the variable is omitted

Oblique rotation methods:

produce factors which are correlated. Similar to orthogonal rotations.

Orthogonal rotation methods:

produce factors which are uncorrelated. This is done either by simplifying rows, thus making as many values in each row as close to zero as possible (e.g. maximizing a variable’s loading on a single factor), or by simplifying columns, thus by making as many values in each column as close to zero as possible (e.g. making the number of high loadings as few as possible).

Do factors solutions provide a good factor solution?

* look at Loadings o factors: >0.4 is high. Has each factor loadings with high values?

* look at communalities above 0.5

* Total variance (treshold 60%)

* rotation might improve interpretability

* Exeption of factor when there is cross-loading (more factors above 0.4)

Which method is the most suitable and provides the best factor solution?

* choose the one with small correlations among components

* one with no cross-loading

* component correlation matrix show correlation between factors

* Unrotated, and rotated Varimax 3 factor solutions are not suitable, because we search for 2 conceptually different factors (idealism vs. realism) >> stated in text description!!!!

Goals when summated scales created

* simplification: representing ultiple aspects of a concept into one measure

* overcoming measurement error

Is scale reliable or not? Which measure?

Cronbach's aplha = 0.68

This value should be sufficient in the case of exploratory research, above 0.6

Criteria to choose PCA and PFA

* the research objective of performing FA

* the amount of prior knowledge about the variance in the variables

Perform PFA when:

- Identification of latent dimensions (underlying factors) is required

- little knowledge exists about specific and error variance

List the possible situations when a respecification of the model is needed

-variable lacks sufficient loading

-variable communality too low

-variable has cross-loading

List the possible remedies available to improve the factor model

-ignore problematic variable(s)

-possible deletion of problematic variable(s)

-alternative rotation of factors

-decrease / increase the number of factors

- modify type of factoring method (PCA or PFA )

Explain how much % of the variance of the dependent variable is explained by the regression.

* look at the model summary and ANOVA table

* Adjusted Rsquare, meaning % of variance of DV is explained by IV

* F-test

* (F statistics and sig.) <> alpha.

* test is significant, meaning that at least one IV contributes to the variance of IV

Which rotation method provides the best factor model?

- there are no cross-loadings anymore

- also, the component correlation matrix show the existence of a correlation between the 2 factors (.417) (specification of Pattern matrix table)

The question on the page originate from the summary of the following study material:

Statistics 2 for IBM | University of Groningen

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Exploratory Factor Analysis

17 important questions on Exploratory Factor Analysis

Difference between PCA and PFA

Intercollinearity test assumptions on correlation FA!

Bartlett’s test of sphericity

Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy (MSA)

Assess the communalities of all variables

Oblique rotation methods:

Orthogonal rotation methods:

Do factors solutions provide a good factor solution?

Which method is the most suitable and provides the best factor solution?

Goals when summated scales created

Is scale reliable or not? Which measure?

Criteria to choose PCA and PFA

Perform PFA when:

List the possible situations when a respecification of the model is needed

List the possible remedies available to improve the factor model

Explain how much % of the variance of the dependent variable is explained by the regression.

Which rotation method provides the best factor model?

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Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy
(MSA)