How to use PC1 of PCA and dim1 of MCA as a predictor in logistic regression model for data reduction
Pooling nominal with numeric variables and running pca on them sounds like conceptual nonsense to me. You use PCA to reduce the dimensionality of the data if the data are numeric. For categorical data analysis, you should use latent class analysis or something along those lines. The fact that your first PC captures only 20 percent of the variance indicates that either you apply the wrong technique or that dimensionality reduction is of little use for these data more generally. The first step should generally be to check the correlations/associations between the variables to inspect whether what you intend to do makes sense. HTH, Daniel
khosoda wrote:
Hi all, I'm trying to do model reduction for logistic regression. I have 13 predictor (4 continuous variables and 9 binary variables). Using subject matter knowledge, I selected 4 important variables. Regarding the rest 9 variables, I tried to perform data reduction by principal component analysis (PCA). However, 8 of 9 variables were binary and only one continuous. I transformed the data by transcan of rms package and did PCA with princomp. PC1 explained only 20% of the variance. Still, I used the PC1 as a predictor of the logistic model and obtained some results. Then, I tried multiple correspondence analysis (MCA). The only one continuous variable was age. I transformed "age" variable to "age_Q" factor variable as the followings.
quantile(mydata.df$age)
0% 25% 50% 75% 100% 53.00 66.75 72.00 76.25 85.00
age_Q <- cut(x17.df$age, right=TRUE, breaks=c(-Inf, 66, 72, 76, Inf),
labels=c("53-66", "67-72", "73-76", "77-85"))
table(age_Q)
age_Q 53-66 67-72 73-76 77-85 26 27 25 26 Then, I used mjca of ca pacakge for MCA.
mjca1 <- mjca(mydata.df[, c("age_Q","sex","symptom", "HT", "DM",
"IHD","smoking","DL", "Statin")])
summary(mjca1)
Principal inertias (eigenvalues):
dim value % cum% scree plot
1 0.009592 43.4 43.4 *************************
2 0.003983 18.0 61.4 **********
3 0.001047 4.7 66.1 **
4 0.000367 1.7 67.8
-------- -----
Total: 0.022111
The dimension 1 explained 43% of the variance. Then, I was wondering
which values I could use like PC1 in PCA. I explored in mjca1 and found
"rowcoord".
mjca1$rowcoord
[,1] [,2] [,3] [,4] [1,] 0.07403748 0.8963482181 0.10828273 1.581381849 [2,] 0.92433996 -1.1497911361 1.28872517 0.304065865 [3,] 0.49833354 0.6482940556 -2.11114314 0.365023261 [4,] 0.18998290 -1.4028117048 -1.70962159 0.451951744 [5,] -0.13008173 0.2557656854 1.16561601 -1.012992485 ......................................................... ......................................................... [101,] -1.86940216 0.5918128751 0.87352987 -1.118865117 [102,] -2.19096615 1.2845448725 0.25227354 -0.938612155 [103,] 0.77981265 -1.1931087587 0.23934034 0.627601413 [104,] -2.37058237 -1.4014005013 -0.73578248 -1.455055095 Then, I used mjca1$rowcoord[, 1] as the followings.
mydata.df$NewScore <- mjca1$rowcoord[, 1]
I used this "NewScore" as one of the predictors for the model instead of original 9 variables. The final logistic model obtained by use of MCA was similar to the one obtained by use of PCA. My questions are; 1. Is it O.K. to perform PCA for data consisting of 1 continuous variable and 8 binary variables? 2. Is it O.K to perform transformation of age from continuous variable to factor variable for MCA? 3. Is "mjca1$rowcoord[, 1]" the correct values as a predictor of logistic regression model like PC1 of PCA? I would appreciate your help in advance. -- Kohkichi Hosoda
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