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factor_analysis_examples [2019/11/20 10:28] – removed hkimscilfactor_analysis_examples [2019/12/06 14:00] – hkimscil
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 +====== 1 ======
 +{{:r:EFA.csv}}
  
 +<code>
 +# read the dataset into R variable using the read.csv(file) function
 +data <- read.csv("http://commres.net/wiki/_media/r/efa.csv")
 +head(data)
 +</code>
 +
 +<code>
 +# install the package
 +# install.packages("psych")
 +# install.packages("GPArotation")
 +# load the package
 +library(psych)
 +library(GPArotation)
 +</code>
 +
 +<code>
 +# calculate the correlation matrix
 +corMat <- cor(data)
 +# display the correlation matrix
 +round(corMat,3)
 +</code>
 +
 +<code>
 +# use fa() to conduct an oblique principal-axis exploratory factor analysis
 +# save the solution to an R variable
 +fa.ini <- fa(r = corMat)
 +# display the solution output
 +fa.ini
 +</code>
 +
 +<code>
 +names(fa.ini)
 +</code>
 +
 +<code>
 +fa.ini$e.values
 +</code>
 +
 +<code>
 +num <- 5
 +fa.5 <- fa(r=corMat, nfactors=num, rotate="varimax", fm="pa")
 +fa.5.oblimin.minres <- fa(r=corMat, nfactors=num, rotate="oblimin", fm="minres")
 +fa.5.vm.minres <- fa(r=corMat, nfactors=num, rotate="varimax", fm="minres")
 +
 +fa.sort(fa.5.oblimin.minres)
 +fa.sort(fa.5.vm.minres)
 +</code>
 +
 +<code>
 +> fa.sort(fa.5.oblimin.minres)
 +Factor Analysis using method =  minres
 +Call: fa(r = corMat, nfactors = num, rotate = "oblimin", fm = "minres")
 +Standardized loadings (pattern matrix) based upon correlation matrix
 +                      MR1   MR2   MR4   MR5   MR3   h2    u2 com
 +Resale_Value         0.73 -0.20  0.08 -0.05 -0.10 0.59 0.413 1.2
 +Price                0.58  0.23 -0.11 -0.01 -0.07 0.35 0.645 1.4
 +Maintenance          0.55  0.11 -0.01  0.26  0.01 0.45 0.549 1.5
 +Fuel_Efficiency      0.38  0.01  0.33  0.23  0.22 0.49 0.512 3.3
 +Safety              -0.31  0.23  0.17  0.07 -0.24 0.21 0.790 3.6
 +Space_comfort       -0.02  0.88  0.04 -0.06  0.03 0.83 0.172 1.0
 +Fuel_Type            0.03  0.52  0.11  0.02 -0.13 0.30 0.699 1.2
 +Technology           0.00  0.28  0.14  0.06  0.01 0.13 0.873 1.6
 +After_Sales_Service -0.01  0.04  0.95 -0.01 -0.01 0.92 0.085 1.0
 +Color                0.03 -0.05  0.02  0.78  0.09 0.67 0.329 1.0
 +Exterior_Looks       0.09  0.05  0.03 -0.54  0.31 0.33 0.669 1.7
 +Testimonials        -0.23  0.04 -0.04  0.08  0.63 0.47 0.535 1.3
 +Test_drive           0.06 -0.02  0.23 -0.06  0.44 0.26 0.745 1.6
 +Product_reviews      0.33  0.25 -0.08  0.12  0.35 0.36 0.642 3.2
 +
 +                       MR1  MR2  MR4  MR5  MR3
 +SS loadings           1.64 1.41 1.21 1.12 0.97
 +Proportion Var        0.12 0.10 0.09 0.08 0.07
 +Cumulative Var        0.12 0.22 0.30 0.38 0.45
 +Proportion Explained  0.26 0.22 0.19 0.18 0.15
 +Cumulative Proportion 0.26 0.48 0.67 0.85 1.00
 +
 + With factor correlations of 
 +      MR1   MR2  MR4   MR5  MR3
 +MR1  1.00 -0.03 0.16  0.25 0.03
 +MR2 -0.03  1.00 0.32 -0.07 0.21
 +MR4  0.16  0.32 1.00  0.13 0.07
 +MR5  0.25 -0.07 0.13  1.00 0.17
 +MR3  0.03  0.21 0.07  0.17 1.00
 +
 +Mean item complexity =  1.8
 +Test of the hypothesis that 5 factors are sufficient.
 +
 +The degrees of freedom for the null model are  91  and the objective function was  2.97
 +The degrees of freedom for the model are 31  and the objective function was  0.34 
 +
 +The root mean square of the residuals (RMSR) is  0.04 
 +The df corrected root mean square of the residuals is  0.06 
 +
 +Fit based upon off diagonal values = 0.97
 +Measures of factor score adequacy             
 +                                                   MR1  MR2  MR4  MR5  MR3
 +Correlation of (regression) scores with factors   0.87 0.92 0.96 0.86 0.79
 +Multiple R square of scores with factors          0.76 0.85 0.92 0.73 0.63
 +Minimum correlation of possible factor scores     0.52 0.70 0.85 0.46 0.26
 +
 +
 +> fa.sort(fa.5.vm.minres)
 +Factor Analysis using method =  minres
 +Call: fa(r = corMat, nfactors = num, rotate = "varimax", fm = "minres")
 +Standardized loadings (pattern matrix) based upon correlation matrix
 +                      MR1   MR2   MR3   MR5   MR4   h2    u2 com
 +Resale_Value         0.69 -0.22 -0.17  0.16  0.01 0.59 0.413 1.5
 +Maintenance          0.61  0.07  0.07  0.07  0.25 0.45 0.549 1.4
 +Price                0.57  0.15 -0.05 -0.04 -0.02 0.35 0.645 1.2
 +Fuel_Efficiency      0.46  0.09  0.28  0.37  0.23 0.49 0.512 3.2
 +Space_comfort        0.02  0.87  0.21  0.00 -0.17 0.83 0.172 1.2
 +Fuel_Type            0.06  0.54 -0.02  0.08 -0.04 0.30 0.699 1.1
 +Technology           0.04  0.32  0.09  0.13  0.03 0.13 0.873 1.5
 +Safety              -0.28  0.30 -0.16  0.11  0.05 0.21 0.790 2.9
 +Testimonials        -0.18  0.04  0.66 -0.05  0.02 0.47 0.535 1.2
 +Test_drive           0.09  0.06  0.43  0.23 -0.07 0.26 0.745 1.7
 +Product_reviews      0.38  0.18  0.41 -0.03  0.07 0.36 0.642 2.4
 +After_Sales_Service  0.06  0.37  0.06  0.88  0.04 0.92 0.085 1.4
 +Color                0.21 -0.05  0.26  0.07  0.74 0.67 0.329 1.4
 +Exterior_Looks      -0.01  0.05  0.20  0.01 -0.54 0.33 0.669 1.3
 +
 +                       MR1  MR2  MR3  MR5  MR4
 +SS loadings           1.72 1.50 1.09 1.03 1.00
 +Proportion Var        0.12 0.11 0.08 0.07 0.07
 +Cumulative Var        0.12 0.23 0.31 0.38 0.45
 +Proportion Explained  0.27 0.24 0.17 0.16 0.16
 +Cumulative Proportion 0.27 0.51 0.68 0.84 1.00
 +
 +Mean item complexity =  1.7
 +Test of the hypothesis that 5 factors are sufficient.
 +
 +The degrees of freedom for the null model are  91  and the objective function was  2.97
 +The degrees of freedom for the model are 31  and the objective function was  0.34 
 +
 +The root mean square of the residuals (RMSR) is  0.04 
 +The df corrected root mean square of the residuals is  0.06 
 +
 +Fit based upon off diagonal values = 0.97
 +Measures of factor score adequacy             
 +                                                   MR1  MR2  MR3  MR5  MR4
 +Correlation of (regression) scores with factors   0.86 0.91 0.80 0.93 0.82
 +Multiple R square of scores with factors          0.75 0.82 0.64 0.87 0.67
 +Minimum correlation of possible factor scores     0.50 0.64 0.27 0.75 0.34
 +> 
 +> 
 +</code>
 +
 +<code>
 +Factor Analysis using method =  minres
 +Call: fa(r = corMat, nfactors = num, rotate = "varimax", fm = "minres")
 +Standardized loadings (pattern matrix) based upon correlation matrix
 +                      MR1   MR2   MR3   MR5   MR4   h2    u2 com
 +----------------------------------------------------------------                      
 +Resale_Value         0.69 -0.22 -0.17  0.16  0.01 0.59 0.413 1.5
 +Maintenance          0.61  0.07  0.07  0.07  0.25 0.45 0.549 1.4
 +Price                0.57  0.15 -0.05 -0.04 -0.02 0.35 0.645 1.2
 +Fuel_Efficiency      0.46  0.09  0.28  0.37  0.23 0.49 0.512 3.2
 +----------------------------------------------------------------
 +Space_comfort        0.02  0.87  0.21  0.00 -0.17 0.83 0.172 1.2
 +Fuel_Type            0.06  0.54 -0.02  0.08 -0.04 0.30 0.699 1.1
 +Technology           0.04  0.32  0.09  0.13  0.03 0.13 0.873 1.5
 +Safety              -0.28  0.30 -0.16  0.11  0.05 0.21 0.790 2.9
 +----------------------------------------------------------------
 +Testimonials        -0.18  0.04  0.66 -0.05  0.02 0.47 0.535 1.2
 +Test_drive           0.09  0.06  0.43  0.23 -0.07 0.26 0.745 1.7
 +Product_reviews      0.38  0.18  0.41 -0.03  0.07 0.36 0.642 2.4
 +----------------------------------------------------------------
 +After_Sales_Service  0.06  0.37  0.06  0.88  0.04 0.92 0.085 1.4
 +----------------------------------------------------------------
 +Color                0.21 -0.05  0.26  0.07  0.74 0.67 0.329 1.4
 +Exterior_Looks      -0.01  0.05  0.20  0.01 -0.54 0.33 0.669 1.3
 +
 +                       MR1  MR2  MR3  MR5  MR4
 +SS loadings           1.72 1.50 1.09 1.03 1.00
 +Proportion Var        0.12 0.11 0.08 0.07 0.07
 +Cumulative Var        0.12 0.23 0.31 0.38 0.45
 +Proportion Explained  0.27 0.24 0.17 0.16 0.16
 +Cumulative Proportion 0.27 0.51 0.68 0.84 1.00
 +</code>
factor_analysis_examples.txt · Last modified: 2022/05/05 15:02 by hkimscil
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