Exploratory Factor Analysis withÂ R can be performed using

**the factanal function.**

In addition to this standard function, some additional facilities are provided by

**fa.promax function.**# I Sample with fa function

> #install the package> install.packages("psych")> #load the package> library(psych)

*> #calculate the correlation matrix**> corMat <- cor(data)**> #display the correlation matrix**> corMat*

> #use fa() to conduct an oblique principal-axis exploratory factor analysis > #save the solution to an R variable> solution <- fa(r = corMat, nfactors = 2, rotate = "oblimin", fm = "pa") > #display the solution output > solution

# II Sample with factanal function

```
# Required packages.
require(psych);
require(foreign);
# Import data from SPSS data file.
personality <- foreign::read.spss("spss\\personality.sav",
to.data.frame = TRUE)
# Factor analysis.
items <- c("ipip1", "ipip2", "ipip3", "ipip4", "ipip5",
"ipip6", "ipip7", "ipip8", "ipip9", "ipip10", "ipip11",
"ipip12", "ipip13", "ipip14", "ipip15", "ipip16", "ipip17",
"ipip18", "ipip19", "ipip20", "ipip21", "ipip22", "ipip23",
"ipip24", "ipip25", "ipip26", "ipip27", "ipip28", "ipip29",
"ipip30", "ipip31", "ipip32", "ipip33", "ipip34", "ipip35",
"ipip36", "ipip37", "ipip38", "ipip39", "ipip40", "ipip41",
"ipip42", "ipip43", "ipip44", "ipip45", "ipip46", "ipip47",
"ipip48", "ipip49", "ipip50") ;
# Descriptive Statistics.
itemDescriptiveStatistics <- sapply(personality[items],
function(x) c(mean=mean(x), sd=sd(x), n = length(x)));
cbind(attr(personality, "variable.labels")[items],
round(t(itemDescriptiveStatistics), 2) );
# Scree plot.
psych::VSS.scree(cor(personality[items]));
# Some other indicators of the number of factors.
psych::VSS(cor(personality[items]), 10,
n.obs = nrow(personality), rotate = "promax");
# Communalities
itemCommunalities <- 1 - dataForScreePlot$uniquenesses;
round(cbind(itemCommunalities), 2);
# List items with low communalities.
itemsWithLowCommunalities <- names(itemCommunalities[
itemCommunalities < .25]);
cat("Items with low communalities (< .25)\n");
problematicItemText <- attr(personality,
"variable.labels")[itemsWithLowCommunalities ];
problematicItemCommunalities <- round(itemCommunalities[
itemsWithLowCommunalities],3);
data.frame(itemText = problematicItemText,
communality = problematicItemCommunalities);
# Variance explained by each factor before rotation.
# (see Proportion Var)
factanal(personality[items], factors = 5, rotation = "none");
# Variance explained by each factor after rotatoin.
# (see Proportion Var)
factanal(personality[items], factors = 5, rotation = "promax");
# Loadings prior to rotation.
fitNoRotation <- factanal(personality[items],
factors = 5, rotation = "none");
print(fitNoRotation$loadings, cutoff = .30, sort = TRUE);
# Loadings after rotation.
fitAfterRotation <- factanal(personality[items],
factors = 5, rotation = "promax");
print(fitAfterRotation$loadings, cutoff = .30, sort = TRUE);
# Correlations between factors
# This assumes use of a correlated rotation method such as promax
factorCorrelationsRegression <- cor(factanal(
personality[items], factors = 5,
rotation = "promax", scores = "regression")$scores);
round(factorCorrelationsRegression,2);
```

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