Chapter 10, Factor Analysis and Principal Component Analysis Video Solutions, Statistics for Marketing and Consumer Research

Problem 1

Open the Trust data-set
a. Assume that questions $\mathrm{q} 12 \mathrm{a}$ to $\mathrm{q} 12 \mathrm{k}$ measure a single latent theoretical construct attitude toward purchasing chicken
b. Using factor analysis, extract the single latent factor using image factoring as a method
c. Check the scree diagram - is it consistent with the choice of retaining a single factor?
d. Interpret the factor loadings - which items show a positive contribution to the factor and which ones a negative contribution?
e. Save the factor scores and show the average by country. Which country shows the highest attitude? Do results change noticeably with different score estimation methods?
f. How much of total variability does the factor reproduce?
g. Exclude items with negative wording (q12c, q12i, q12k) and compute the alpha reliability index (HINT: use SCALE / RELIABILITY ANALYSIS).
h. Run factor analysis again to look for a single factor measuring overall attitude. Do results improve?

Jameson Kuper

Numerade Educator

04:04

Problem 2

Open the Trust data-set
a. Consider the attributes of chicken safety (q21a to q211) and assume they measure various dimension of safety
b. Using factor analysis and the alpha factoring method on the correlation matrix, extract the number of factors that seems most appropriate and show the scree diagram
c. Use the VARIMAX rotation and label the factors according to the factor loadings
d. Consider the table of communalities - which variable is best explained? Which one is least explained by the retained factors?
e. Draw a bar chart showing the level of the factor scores for each country
f. How do result change if maximum likelihood is chosen instead of alpha factoring?

Jameson Kuper

Numerade Educator

Problem 3

Open the EFS data-set
a. Consider all food expenditure items between c11111 and c11941
b. Summarize the 58 expenditure items into a reduced number of components able to explain at least $60 \%$ of the original variability. How many components are retained? How many should be retained to explain $75 \%$ of the variability?
c. Try and interpret the component loadings for the first three components
d. Run the analysis using alternatively the covariance and correlation matrix. Which one should be preferred? Which one produces the best results?
e. Extract the component scores and check their correlation with anonymized income (incanon)

Check back soon!