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--- factor_analysis_examples [2019/11/20 08:52] – [Personality] hkimscil
+++ factor_analysis_examples [2022/05/05 14:57] – [2] hkimscil
@@ Line 1: / Line 1: @@
-====== FA e.gs ======
+====== EFA datasets: Car buying factors ======
-====== Personality ======
+{{:r:EFA.csv}}
 <code>
-d <- read.table("http://commres.net/wiki/_media/r/personality0.txt")
+# 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>
-살펴보기 (head)
-구조및성질 (str)
-상관관계 도식화 (corrplot)
-  * require corrplot package
 <code>
-install.packages("corrplot") # if not installed
+# install the package
-library(corrplot)
+# install.packages("psych")
-corrplot(cor(d), order = "hclust", tl.col='black', tl.cex=.75)
+# install.packages("GPArotation")
-</code>
+# load the package
+library(psych)
+library(GPArotation)
+</code>
-fa 펑션 factor analysis
 <code>
-library(psych)
+# calculate the correlation matrix
-d.fa <- fa(d, rotate="none") # fa test with no rotation
+corMat <- cor(data)
-names(d.fa) # to see what comes with the output d.fa
+# display the correlation matrix
+round(corMat,3)
 </code>
-check out the output.
 <code>
-d.fa
+# 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>
-compare the output to d.fa$communality
 <code>
-d.fa$communality
+names(fa.ini)
 </code>
-for better output
 <code>
-data.frame(d.fa$communality)
+fa.ini$e.values
 </code>
-d.fa 아웃풋처럼 round 처리
 <code>
-round(data.frame(d.fa$communality),3)
+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>
-check out the uniqueness too
+<code>
-<WRAP info 70%>
+> fa.sort(fa.5.oblimin.minres)
-uniqueness check
+Factor Analysis using method =  minres
-직접 해 보기
+Call: fa(r = corMat, nfactors = num, rotate = "oblimin", fm = "minres")
-</WRAP>
+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>
+====== 2 ======
+<code>
+food <- read.csv("http://commres.net/wiki/_media/r/food-texture.csv",
+                 row.names = "X")
+str(food)
+</code>
+<code>
+food.fa <- factanal(food, factors = 2)
+food.fa
+food.fa$uniquenesses
+apply(food.fa$loadings^2,1,sum) # communality
+- apply(food.fa$loadings^2,1,sum) # 1 - communality = uniq
+</code>
+<code>
+Lambda <- food.fa$loadings
+Psi <- diag(food.fa$uniquenesses)
+S <- food.fa$correlation
+Sigma <- Lambda %*% t(Lambda) + Psi
+</code>
+<code>
+round(S - Sigma, 6)
+</code>
+<code>
+food.fa.none <- factanal(food, factors = 2, rotation = "none")
+food.fa.varimax <- factanal(food, factors = 2, rotation = "varimax")
+food.fa.promax <- factanal(food, factors = 2, rotation = "promax")
+par(mfrow = c(1,3))
+plot(food.fa.none$loadings[,1],
+     food.fa.none$loadings[,2],
+     xlab = "Factor 1",
+     ylab = "Factor 2",
+     ylim = c(-1,1),
+     xlim = c(-1,1),
+     main = "No rotation")
+abline(h = 0, v = 0)
+plot(food.fa.varimax$loadings[,1],
+     food.fa.varimax$loadings[,2],
+     xlab = "Factor 1",
+     ylab = "Factor 2",
+     ylim = c(-1,1),
+     xlim = c(-1,1),
+     main = "Varimax rotation")
+text(food.fa.varimax$loadings[,1]-0.08,
+     food.fa.varimax$loadings[,2]+0.08,
+      colnames(food),
+      col="blue")
+abline(h = 0, v = 0)
+plot(food.fa.promax$loadings[,1],
+     food.fa.promax$loadings[,2],
+     xlab = "Factor 1",
+     ylab = "Factor 2",
+     ylim = c(-1,1),
+     xlim = c(-1,1),
+     main = "Promax rotation")
+abline(h = 0, v = 0)
+par(mfrow = c(1,1))
+</code>