R help - Aug 2011 - How to use PC1 of PCA and dim1 of MCA as a predictor in logistic regression model for data reduction

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

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$rowcoord[, 1]" the correct values as a predictor of
> logistic regression model like PC1 of PCA?
> 
> I would appreciate your help in advance.
> 
> --
> Kohkichi Hosoda
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
--
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On Aug 17, 2011 khosoda wrote:
> 1. Is it O.K. to perform PCA for data consisting of 1 continuous 
> variable and 8 binary variables? 
> 2. Is it O.K to perform transformation of age from continuous variable 
> to factor variable for MCA? 
> 3. Is "mjca1$rowcoord[, 1]" the correct values as a predictor of 
> logistic regression model like PC1 of PCA?
Hi Kohkichi,

If you want to do this, i.e. PCA-type analysis with different
variable-types, then look at dudi.mix() in package ade4 and homals() in
package homals.

Regards, Mark.

-----
Mark Difford (Ph.D.)
Research Associate
Botany Department
Nelson Mandela Metropolitan University
Port Elizabeth, South Africa
--
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Dear Mark,

Thank you very much for your mail. This is what I really wanted!
I tried dudi.mix in ade4 package.

 > ade4plaque.df <- x18.df[c("age", "sex",
"symptom", "HT", "DM", "IHD",
"smoking", "DL", "Statin")]

 > head(ade4plaque.df)
   age sex      symptom       HT       DM      IHD  smoking 
hyperlipidemia   Statin
1  62   M asymptomatic positive negative negative positive 
positive positive
2  82   M  symptomatic positive negative negative negative 
positive positive
3  64   M asymptomatic negative positive negative negative 
positive positive
4  55   M  symptomatic positive positive positive negative 
positive positive
5  67   M  symptomatic positive negative negative negative 
negative positive
6  79   M asymptomatic positive positive negative negative 
positive positive

 > x18.dudi.mix <- dudi.mix(ade4plaque.df)
 > x18.dudi.mix$eig
[1] 1.7750557 1.4504641 1.2178640 1.0344946 0.8496640 0.8248379 
0.7011151 0.6367328 0.5097718
 > x18.dudi.mix$eig[1:9]/sum(x18.dudi.mix$eig)
[1] 0.19722841 0.16116268 0.13531822 0.11494385 0.09440711 0.09164866 
0.07790168 0.07074809 0.05664131

Still first component explained only 19.8% of the variances, right?

Then, I investigated values of dudi.mix corresponding to PC1 of PCA. 
Help file say;
l1	 principal components, data frame with n rows and nf columns
li	 row coordinates, data frame with n rows and nf columns

So, I guess I should use x18.dudi.mix$l1[, 1].
Am I right?

Or should I use multiple correpondence analysis because the first plane 
explained 43% of the variance?

Thank you for your help in advance.

Kohkichi


(11/08/18 18:33), Mark Difford wrote:
> On Aug 17, 2011 khosoda wrote:
>
>> 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?
>
> Hi Kohkichi,
>
> If you want to do this, i.e. PCA-type analysis with different
> variable-types, then look at dudi.mix() in package ade4 and homals() in
> package homals.
>
> Regards, Mark.
>
> -----
> Mark Difford (Ph.D.)
> Research Associate
> Botany Department
> Nelson Mandela Metropolitan University
> Port Elizabeth, South Africa
> --
> View this message in context:
http://r.789695.n4.nabble.com/How-to-use-PC1-of-PCA-and-dim1-of-MCA-as-a-predictor-in-logistic-regression-model-for-data-reduction-tp3750251p3752168.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

-- 
*************************************************
????????????? ????????
??? ??
?
??650-0017?????????7??5-1
     Phone: 078-382-5966
     Fax  : 078-382-5979
     E-mail address
         Office: khosoda at med.kobe-u.ac.jp
	Home  : khosoda at venus.dti.ne.jp

Dear Mark,

Thank you very much for your advice.
I will try it.

I really appreciate your all kind advice.
Thanks a lot again.

Best regards,

Kohkichi


(11/08/19 22:28), Mark Difford wrote:
> On Aug 19, 2011 khosoda wrote:
>
>> I used x10.homals4$objscores[, 1] as a predictor for logistic
regression
>> as in the same way as PC1 in PCA.
>> Am I going the right way?
>
> Hi Kohkichi,
>
> Yes, but maybe explore the "sets=" argument (set
"Response" as the target
> variable and the others as the predictor variables). Then use Dim1 scores.
> Also think about fitting a rank-1 restricted model, combined with the
sets> option.
>
> See the vignette to the package and look at
>
> @ARTICLE{MIC98,
>    author = {Michailides, G. and de Leeuw, J.},
>    title = {The {G}ifi system of descriptive multivariate analysis},
>    journal = {Statistical Science},
>    year = {1998},
>    volume = {13},
>    pages = {307--336},
>    abstract = {}
> }
>
> Regards, Mark.
>
> -----
> Mark Difford (Ph.D.)
> Research Associate
> Botany Department
> Nelson Mandela Metropolitan University
> Port Elizabeth, South Africa
> --
> View this message in context:
http://r.789695.n4.nabble.com/How-to-use-PC1-of-PCA-and-dim1-of-MCA-as-a-predictor-in-logistic-regression-model-for-data-reduction-tp3750251p3755163.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>