factor analysis using R

Question

Im trying to do a factor analysis using R with varimax rotation, but not successful. I run the same exact data on SAS and can get result.

in R, if I use

fa(r=cor(m1), nfactors=8, fm="ml", rotate="varimax")

I will get

In smc, the correlation matrix was not invertible, smc's returned as 1s
In smc, the correlation matrix was not invertible, smc's returned as 1s
Error in optim(start, FAfn, FAgr, method = "L-BFGS-B", lower = 0.005,  : 
  L-BFGS-B needs finite values of 'fn'
In addition: Warning messages:
1: In cor.smooth(R) : Matrix was not positive definite, smoothing was done
2: In cor.smooth(R) : Matrix was not positive definite, smoothing was done
3: In log(e) : NaNs produced

if I use

factanal(cor(m1), factors=8)

i will get

Error in solve.default(cv) : 
  system is computationally singular: reciprocal condition number = 4.36969e-19

Can anyone help me how to do factor analysis successfully using R. Thanks.

Tq in advance

Answer 1

The warnings and errors indicates that your matrix is singular, thus no solution exists to the optimization problem.

This means you need to use a different method of factor analysis. Using fa() in package psych you have two alternatives to perform factor analysis given a singular matrix:

• pa (Principal axis factor analysis)
• minres (Minimum residual factor analysis)

However, given your data, only minres seems to yield useful results, albeit with many health warnings:

library(psych)
library(GPArotation)
fa(r=cor(m1), nfactors=8, rotate="varimax", SMC=FALSE, fm="minres")

This gives:

In smc, the correlation matrix was not invertible, smc's returned as 1s
In factor.stats, the correlation matrix is singular, an approximation is used
In factor.scores, the correlation matrix is singular, an approximation is used
I was unable to calculate the factor score weights, factor loadings used instead
Factor Analysis using method =  minres
Call: fa(r = cor(m1), nfactors = 8, rotate = "varimax", SMC = FALSE, 
    fm = "minres")
Standardized loadings (pattern matrix) based upon correlation matrix
                MR1   MR3   MR2   MR6   MR5   MR4   MR7   MR8   h2    u2
Adorable       0.64  0.69  0.04  0.26  0.05  0.04  0.01  0.14 0.98 0.020
Appealing      0.69  0.66  0.06  0.22  0.06  0.00  0.03  0.08 0.98 0.021
Beautiful      0.39  0.82 -0.16  0.11  0.24 -0.05 -0.07 -0.08 0.93 0.071
Boring        -0.49 -0.70  0.33 -0.27  0.01  0.03  0.11 -0.16 0.95 0.054
Calm           0.76  0.42  0.33  0.10  0.28 -0.04  0.02  0.05 0.96 0.038
Charming       0.62  0.75  0.04  0.15  0.07 -0.03  0.03  0.01 0.98 0.024
Chic           0.07  0.94 -0.13  0.17 -0.03  0.12 -0.02  0.02 0.95 0.048
Childish      -0.13  0.00  0.04  0.04 -0.04  0.98  0.01  0.00 0.98 0.016
Classic        0.82  0.16  0.28 -0.31  0.14  0.10  0.16  0.06 0.94 0.058
Comfortable    0.66  0.50  0.19  0.39  0.27 -0.02  0.13  0.08 0.97 0.033
Cool           0.81  0.43  0.03  0.32  0.00  0.01 -0.03  0.20 0.98 0.016
Creative       0.78  0.37 -0.41  0.14 -0.05  0.06 -0.05  0.20 0.98 0.024
Crowded       -0.34 -0.12 -0.77 -0.13 -0.18  0.04  0.44  0.00 0.96 0.041
Cute           0.50  0.78  0.03  0.18  0.07  0.25 -0.09  0.14 0.98 0.024
Elegant        0.67  0.70  0.07 -0.04  0.10 -0.14  0.03  0.07 0.98 0.021
Feminine       0.09  0.96  0.00  0.01  0.01 -0.02  0.04  0.03 0.93 0.069
Fun            0.58  0.45 -0.21  0.56  0.01  0.20 -0.06 -0.08 0.95 0.054
Futuristic     0.91  0.26 -0.10  0.14 -0.07 -0.03 -0.18 -0.08 0.98 0.021
Gorgeous       0.82  0.52 -0.04  0.14  0.05 -0.09 -0.08 -0.01 0.98 0.019
Impressive     0.82  0.48 -0.02  0.23  0.05  0.00 -0.10  0.07 0.98 0.021
Interesting    0.72  0.55  0.05  0.34  0.15  0.01 -0.13  0.03 0.98 0.020
Light          0.20  0.49  0.30  0.72  0.22  0.03 -0.03  0.02 0.93 0.065
Lively         0.62  0.66 -0.06  0.37  0.16  0.00 -0.04 -0.03 0.98 0.021
Lovely         0.68  0.68 -0.04  0.12  0.19 -0.03 -0.08  0.01 0.98 0.019
Luxury         0.89  0.36 -0.02  0.00  0.08 -0.15 -0.04 -0.07 0.96 0.036
Masculine      0.91 -0.06 -0.05  0.24  0.05 -0.08  0.00 -0.17 0.94 0.063
Mystic         0.95  0.05  0.13  0.01 -0.03  0.00 -0.10  0.00 0.93 0.069
Natural        0.47  0.32  0.42  0.19  0.57 -0.17  0.23  0.02 0.95 0.050
Neat          -0.07  0.06  0.27  0.08  0.93 -0.01 -0.06 -0.01 0.96 0.042
Oldfashioned  -0.64 -0.54  0.20 -0.31  0.16  0.13  0.27 -0.16 0.97 0.026
Plain         -0.23 -0.19  0.88 -0.06  0.18  0.06  0.14 -0.14 0.94 0.062
Pretty         0.66  0.68  0.06  0.17  0.16 -0.11  0.01  0.10 0.97 0.029
Professional   0.82  0.41  0.09  0.18  0.16 -0.18  0.04  0.13 0.96 0.039
Refreshing     0.54  0.58  0.19  0.45  0.30 -0.03  0.10  0.07 0.98 0.021
Relaxing       0.56  0.65  0.34  0.26  0.21 -0.04  0.13 -0.03 0.97 0.026
Sexy           0.35  0.81  0.27  0.05 -0.01 -0.24  0.01 -0.19 0.94 0.056
Simple         0.08  0.01  0.96  0.08  0.09  0.02  0.04  0.12 0.96 0.041
Sophisticated  0.86  0.44 -0.01  0.04 -0.04 -0.12  0.08  0.05 0.96 0.040
Stylish        0.77  0.58  0.06  0.15  0.00 -0.07  0.07  0.08 0.97 0.030
Surreal        0.85  0.39  0.14  0.18 -0.05  0.02  0.08 -0.02 0.93 0.067

                        MR1   MR3  MR2  MR6  MR5  MR4  MR7  MR8
SS loadings           16.50 11.81 3.57 2.45 1.89 1.34 0.55 0.37
Proportion Var         0.41  0.30 0.09 0.06 0.05 0.03 0.01 0.01
Cumulative Var         0.41  0.71 0.80 0.86 0.91 0.94 0.95 0.96
Proportion Explained   0.43  0.31 0.09 0.06 0.05 0.03 0.01 0.01
Cumulative Proportion  0.43  0.74 0.83 0.89 0.94 0.98 0.99 1.00

Test of the hypothesis that 8 factors are sufficient.

The degrees of freedom for the null model are  780  and the objective function was  NaN
The degrees of freedom for the model are 488  and the objective function was  NaN 

The root mean square of the residuals (RMSR) is  0.01 
The df corrected root mean square of the residuals is  0.02 

Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                               MR1 MR3 MR2  MR6  MR5  MR4  MR7  MR8
Correlation of scores with factors               1   1   1 1.00 1.00 1.00 1.00 0.99
Multiple R square of scores with factors         1   1   1 1.00 1.00 1.00 0.99 0.98
Minimum correlation of possible factor scores    1   1   1 0.99 0.99 0.99 0.98 0.97
Warning messages:
1: In cor.smooth(R) : Matrix was not positive definite, smoothing was done
2: In log(det(m.inv.r)) : NaNs produced
3: In log(det(r)) : NaNs produced
4: In cor.smooth(r) : Matrix was not positive definite, smoothing was done
5: In cor.smooth(r) : Matrix was not positive definite, smoothing was done