How many factors should be extracted based on PCA and EFA?

Question

I have df.core.new dataframe with 60 items.
I use PCA to explore the factors:

   psych::principal(df.core.new,rotate ='promax')
Principal Components Analysis
Call: psych::principal(r = df.core.new, rotate = "promax")
Standardized loadings (pattern matrix) based upon correlation matrix
      PC1      h2   u2 com
q01  0.06 3.5e-03 1.00   1
q02  0.12 1.6e-02 0.98   1
q04 -0.26 7.0e-02 0.93   1
q05 -0.06 3.3e-03 1.00   1
q06  0.09 7.6e-03 0.99   1
q07  0.09 7.6e-03 0.99   1
q08  0.01 2.7e-05 1.00   1
q09  0.12 1.3e-02 0.99   1
q10  0.12 1.5e-02 0.99   1
q11  0.09 8.0e-03 0.99   1
q12  0.06 3.6e-03 1.00   1
q13 -0.03 1.2e-03 1.00   1
q14  0.02 6.1e-04 1.00   1
q15  0.11 1.1e-02 0.99   1
q16  0.32 9.9e-02 0.90   1
q17  0.12 1.4e-02 0.99   1
q18  0.19 3.7e-02 0.96   1
q20  0.20 4.2e-02 0.96   1
q21  0.28 7.9e-02 0.92   1
q22  0.13 1.8e-02 0.98   1
q23  0.40 1.6e-01 0.84   1
q24  0.38 1.4e-01 0.86   1
q25  0.34 1.2e-01 0.88   1
q26  0.34 1.2e-01 0.88   1
q27  0.35 1.2e-01 0.88   1
q28  0.50 2.5e-01 0.75   1
q29  0.49 2.4e-01 0.76   1
q30  0.33 1.1e-01 0.89   1
q31  0.34 1.2e-01 0.88   1
q32  0.23 5.5e-02 0.95   1
q33  0.26 6.7e-02 0.93   1
q34  0.13 1.6e-02 0.98   1
q36  0.45 2.0e-01 0.80   1
q38  0.42 1.7e-01 0.83   1
q39  0.46 2.1e-01 0.79   1
q40  0.26 6.7e-02 0.93   1
q41  0.41 1.7e-01 0.83   1
q42  0.26 6.7e-02 0.93   1
q44  0.29 8.2e-02 0.92   1
q46  0.62 3.9e-01 0.61   1
q47  0.35 1.2e-01 0.88   1
q48  0.70 4.8e-01 0.52   1
q49  0.69 4.8e-01 0.52   1
q51  0.60 3.6e-01 0.64   1
q52  0.71 5.0e-01 0.50   1
q53  0.49 2.4e-01 0.76   1
q54  0.52 2.7e-01 0.73   1
q55  0.71 5.0e-01 0.50   1
q56  0.65 4.2e-01 0.58   1
q57  0.59 3.4e-01 0.66   1
q58  0.42 1.8e-01 0.82   1
q59  0.70 4.9e-01 0.51   1
q60  0.64 4.1e-01 0.59   1

                PC1
SS loadings    8.11
Proportion Var 0.15

Mean item complexity =  1
Test of the hypothesis that 1 component is sufficient.

The root mean square of the residuals (RMSR) is  0.12 
 with the empirical chi square  62848.22  with prob <  0 

Fit based upon off diagonal values = 0.55     

In PCA, suggest 1 factor, then I explore the factors number:

    > psych::fa.parallel(df.core.new,fa="both",n.iter=100)
Parallel analysis suggests that the number of factors =  8  and the number of components =  7   

1.How many factors should I use in EFA?
2.If 7 factors,what the usage of PCA result?I really don't know when should I use PCA. PCA seemed not worthy to consider.

Answer 1

principal in the psych package extracts one component by default. It did not tell you there was one component, you told it to extract one component.

Determining the number of factors is a complex task; there are several statistical guidelines (e.g. eigenvalue over 1, scree test, proportion of variance) and you can read about them in any book on factor analysis. But really, the way to do it is to look at various solutions and see which one makes the most substantive sense. You have to use your subject matter knowledge to figure this out. Of course, sometimes, the answer is obvious. But usually not.