The R program for chapter 14.
Creating the hypothetical data set of pairs of data from a multivariate normal distribution with N(100, 100), N(50, 50) and rho=0.707.
rm2 <- rmvnorm(100, mean=c(100, 50), cov=matrix(c(100, 50, 50, 50), 2))
Fig. 14.1, p. 371.
Scatterplot of Norm1 versus Norm2.
plot(rm2[, 1], rm2[, 2], xlab="Norm1", ylab="Norm2")
Table 14.1, p. 372.
Sample statistics for the hypothetical data set.
apply( rm2, 2, mean)
[1] 100.52162 50.18179
apply( rm2, 2, stdev)
[1] 10.304296 7.183615
apply( rm2, 2, var)
[1] 106.17852 51.60432
cor(rm2)
[,1] [,2]
[1,] 1.0000000 0.6914247
[2,] 0.6914247 1.0000000
Principal components, middle p. 373.
pr1 <- princomp(rm2) loadings(pr1) Comp.1 Comp.2 X1 -0.857 0.515 X2 -0.515 -0.857 #eigenvalues: pr1.eigen <- pr1$sdev^2 print(pr1.eigen) Comp.1 Comp.2 135.5229 20.68208
Creating a subset of the depression data set. To minimize the typing we will attach the depression data set and after creating the subset we will detach it.
attach(depress) cesd.subset <- data.frame(c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20) detach(depress)
Creating the data set std.cesd which contains the standardizing the variables c1-c20 from the cesd.subset data set because the princomp function does not automatically standardize the variables.
std.cesd <- cesd.subset std.cesd$c1 <- cesd.subset$c1/stdev(cesd.subset$c1) std.cesd$c2 <- cesd.subset$c2/stdev(cesd.subset$c2) std.cesd$c3 <- cesd.subset$c3/stdev(cesd.subset$c3) std.cesd$c4 <- cesd.subset$c4/stdev(cesd.subset$c4) std.cesd$c5 <- cesd.subset$c5/stdev(cesd.subset$c5) std.cesd$c6 <- cesd.subset$c6/stdev(cesd.subset$c6) std.cesd$c7 <- cesd.subset$c7/stdev(cesd.subset$c7) std.cesd$c8 <- cesd.subset$c8/stdev(cesd.subset$c8) std.cesd$c9 <- cesd.subset$c9/stdev(cesd.subset$c9) std.cesd$c10 <- cesd.subset$c10/stdev(cesd.subset$c10) std.cesd$c11 <- cesd.subset$c11/stdev(cesd.subset$c11) std.cesd$c12 <- cesd.subset$c12/stdev(cesd.subset$c12) std.cesd$c13 <- cesd.subset$c13/stdev(cesd.subset$c13) std.cesd$c14 <- cesd.subset$c14/stdev(cesd.subset$c14) std.cesd$c15 <- cesd.subset$c15/stdev(cesd.subset$c15) std.cesd$c16 <- cesd.subset$c16/stdev(cesd.subset$c16) std.cesd$c17 <- cesd.subset$c17/stdev(cesd.subset$c17) std.cesd$c18 <- cesd.subset$c18/stdev(cesd.subset$c18) std.cesd$c19 <- cesd.subset$c19/stdev(cesd.subset$c19) std.cesd$c20 <- cesd.subset$c20/stdev(cesd.subset$c20)
Table 14.2, p. 380.
Principal component analysis for the standardized CESD scale items.
pr.std <- princomp(std.cesd)
pr.std$coef
<output omitted>
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
c1 0.277 0.145 0.119 -0.120 0.181 -0.388 0.197
c2 0.313 -0.248 -0.101 -0.131 -0.114
c3 0.268 0.155 -0.247 -0.218 -0.109 -0.111 0.246 -0.393
c4 0.244 0.319 0.177 -0.173 0.141 0.153 -0.128 0.410
c5 0.287 0.138 -0.279
c6 0.221 0.224 -0.182 -0.340 0.151 0.255 0.274 -0.339
c7 0.284 0.164 -0.196
c8 0.108 0.305 0.110 0.557 -0.321 0.381 -0.115 -0.374
c9 0.176 0.169 -0.396 0.535 -0.127 -0.136 -0.120
c10 0.277 0.365 0.163 0.233
c11 0.243 0.105 -0.131 0.242 0.124 0.364
c12 0.179 -0.230 0.163 -0.145 -0.367 0.461 -0.304 0.254 0.391
c13 0.126 -0.213 0.265 0.540 0.191 -0.452 0.302
c14 0.180 -0.401 -0.101 0.246 0.171 0.508 0.229
c15 0.200 -0.210 0.270 -0.390 -0.356 -0.288
c16 0.192 -0.417 -0.185 -0.202 -0.305 -0.200
c17 0.210 -0.390 0.318 0.204 -0.382
c18 0.172 0.202 0.275 0.550 0.292 -0.474
c19 0.131 -0.633 -0.335 0.158 -0.117 -0.316 0.162
c20 0.236 0.228 -0.193 0.240 -0.291 -0.177 0.102 0.375
#Eigenvalues:
pr.std.eigen <- pr.std$sdev^2
print(pr.std.eigen)
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8
7.03142 1.480516 1.227321 1.06206 1.009188 0.96417 0.9435959 0.7666211
#Correlations:
r.pr <- 0.5/sqrt(pr.std.eigen)
print(r.pr)
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7
0.1885595 0.4109258 0.4513266 0.4851717 0.4977186 0.5092056 0.514727
Fig. 14.5, p. 381
Eigenvalues.
plot(pr.std.eigen)
