1. Performance Tests in Guide Dogs
Factor Analysis
Performance Tests in Guide Dogs
R. Leotta, B. Voltini, M. Mele, M.C. Curadi, M. Orlandi, P. Secchiari (2006). ``Latent Vaiable Models on Performance Tests of Guide Dogs. 1. Factor Analysis,’’ Italian Journal of Animal Sciences, Vol. 5, pp

2. Data Description
Data collected on n = 143 guide dogs on p = 11 variables:
X1 ≡ Coming on Recall
X2 ≡ Retrieving
X3 ≡ Dominance
X4 ≡ Following Aptitude
X5 ≡ Curiosity to big windowed box in center of room
X6 ≡ Reaction to Noise
X7 ≡ Walking on anomalous surface as grilled ground
X8 ≡ Passage on a weighing plank
X9 ≡ Umbrella Test
X10 ≡ Reaction to rolling Trolley
X11 ≡ Reaction to a big puppet dog
Variables scored on 1-5 scale, with 1 being unfavorable for working dog

3. Correlation Matrix, Means, Standard Deviations
Due to the scaling of the variables, very little difference between factor analyses of the covariance matrix (S) or
Correlation matrix ® would occur. We will use R.

4. Orthogonal Factor Model - I

5. Orthogonal Factor Model - II

6. Estimation – Principal Factor Method - I

7. Estimation – Principal Factor Method - II

8. Eigenvalues and Eigenvectors of R
First two eigenvalues account for 43% of total variation, first four account for 62%
To be able to test for adequacy of m factors, need 0.5((p-m)2 – (p+m)) = 0.5((11-m)2 – (11+m)) > 0 => m ≤ 6
Authors used m = 2 in their analysis

9. Principal Factor Estimates of L, Communalities and Y for m = 2, 4
The two columns of L2 are the unrotated factor loadings for the 2-factor model.
The first may interpreted as an overall sum of the scores for the dog (similar positive coefficients for all 11 variables)
The second may be interpreted as a contrast between variables X1:X5 and X6:X10
The 4 factor model has two additional sets of factor loadings.

10. Maximum Likelihood Estimates of L, Communalities and Y for m = 2, 4
The two columns of L2 are the unrotated factor loadings for the 2-factor model.
The first may interpreted as an overall sum of the scores for the dog (similar positive coefficients for all 11 variables)
The second may be interpreted as a contrast between variables X1:X5 and X6:X10
The 4 factor model has two additional sets of factor loadings.
Note that for the ML estimates, the first 2 sets of factor loadings differ for the 2- and 4-factor models

11. Large-Sample Test for # of Common Factors (m)
Test Stat DF X2(.05) P-value m= m=

12. Plot of Factor Loadings for 2 Factor Model
Some variables have high loadings on both factors. Factor 2 is “bi-polar” with positive and negative loadings
Will rotate axes so that there are possibly clearer interpretations for the 2 factors.
Varimax rotation

13. Rotated Factor Loadings
Variables 5:10 Load High (> .35) on Factor 1,
Variables 1:5 Load High on Factor 2
Less overlap and bi-polarity removed

14. Estimating Factor Scores – Weighted Least Squares

15. Guide Dog Example