Multidimensionality: What does it mean?

Factor Analysis in R

Jennifer Brussow

Psychometrician

Factors = constructs

Construct: an attribute of interest
- Can't be directly measured
Examples:
- Self-determination
- Reasoning ability
- Political affiliation
- Extraversion

Factors = constructs

Distribution equals theory

Interpreting confirmatory analyses

Flowchart of CFA: theory, confirmatory analysis, and interpretation

Interpreting exploratory analyses

Flowchart of EFA: no theory, exploratory analysis, and interpretation

# Run the EFA with six factors (as indicated by your scree plot)
EFA_model <- fa(bfi_EFA, nfactors = 6)

# View results from the model object
EFA_model

Factor Analysis using method =  minres
Call: fa(r = bfi_EFA, nfactors = 6)
Standardized loadings (pattern matrix) based upon correlation matrix
     MR2   MR1   MR3   MR5   MR4   MR6   h2   u2 com
A1  0.10 -0.09  0.07 -0.56  0.11  0.28 0.35 0.65 1.8
A2  0.05 -0.01  0.08  0.69 -0.02  0.01 0.49 0.51 1.0
A3 -0.04 -0.13  0.03  0.57  0.11  0.09 0.47 0.53 1.3
A4 -0.05 -0.08  0.19  0.35 -0.07  0.19 0.25 0.75 2.5
A5 -0.17 -0.20  0.00  0.42  0.20  0.17 0.46 0.54 2.7
C1  0.01  0.07  0.54 -0.07  0.21  0.07 0.35 0.65 1.4
C2  0.09  0.14  0.63  0.01  0.17  0.16 0.46 0.54 1.4
...

EFA_model$loadings

Loadings:
   MR2    MR1    MR3    MR5    MR4    MR6   
A1                      -0.559  0.109  0.285
A2                       0.685              
A3        -0.129         0.569  0.113       
A4                0.193  0.348         0.189
A5 -0.172 -0.200         0.421  0.201  0.166
C1                0.542         0.214       
C2         0.138  0.631         0.170  0.157
C3         0.128  0.532  0.110              
C4               -0.683         0.118  0.229
C5  0.103  0.172 -0.599         0.131       
E1 -0.158  0.589  0.133 -0.116         0.106
E2         0.694                            
E3        -0.343         0.104  0.468       
E4        -0.565         0.184         0.255
E5  0.171 -0.408  0.275         0.216

Factor scores

head(EFA_model$scores)

             MR2         MR1        MR3         MR5        MR4         MR6
65237         NA          NA         NA          NA         NA          NA
61825  0.4731267  2.21345215 -2.7650759 -2.72096751 -0.9357389 -1.54036174
67417  0.5217166  0.15834190 -2.1790559  0.47053433  0.4909513 -0.49268634
62051 -1.3333104 -1.32520518  1.0266578 -0.07063958 -0.3670002 -0.07978805
63767 -1.6844911 -1.45769993  1.7776350  1.01101859  0.7490857 -0.35677764
66734 -0.7014448  0.06174358 -0.3530992 -0.05968920 -0.4435187 -0.75311430

WARNING: Do not interpret factor scores until you have a theory!

Let's practice!

Factor Analysis in R