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--- factor_analysis_examples [2019/12/06 14:01] – hkimscil
+++ factor_analysis_examples [2022/05/05 15:02] (current) – [2] hkimscil
@@ Line 180: / Line 180: @@
 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.ini <- fa(food)
+food.ini$e.values  # we decide to get two factors based on eigenvalues
+</code>
+<code>
+food.fa <- factanal(food, factors = 2)
+food.fa
+food.fa$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>