Nonlinear Canonical Correlation Analysis

[MaaikeSmits]

I want to compare 3 clusters of cases (persons) on various continuous variables, in order to see if differences occur in how the continuous variables are associated with clustermembership (categorical). I wanted to use canonical correlations, however I find that this is impossible with categorical variables. The Nonlinear Canonical Correlation Analysis seem be a solution, but I can't find any information on how to perform this analysis or interpret the output in SPSS version 22.0 Can anyone be of any assistance regarding information on this procedure, or does anyone have alternative ideas on the analysis of choice?
Kind Regards,
Maaike

[Ryan]

A mixed model would work for this scenario quite nicely.

Ryan

Sent from my iPhone

> On Oct 12, 2015, at 7:17 AM, MaaikeSmits <[hidden email]> wrote:
>
> I want to compare 3 clusters of cases (persons) on various continuous
> variables, in order to see if differences occur in how the continuous
> variables are associated with clustermembership (categorical). I wanted to
> use canonical correlations, however I find that this is impossible with
> categorical variables. The Nonlinear Canonical Correlation Analysis seem be
> a solution, but I can't find any information on how to perform this analysis
> or interpret the output in SPSS version 22.0 Can anyone be of any assistance
> regarding information on this procedure, or does anyone have alternative
> ideas on the analysis of choice?
> Kind Regards,
> Maaike
>
>
>
> --
> View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Nonlinear-Canonical-Correlation-Analysis-tp5730762.html
> Sent from the SPSSX Discussion mailing list archive at Nabble.com.
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[MaaikeSmits]

Thank you Ryan for your response. I should add that I tried comparing the clusters by means of mixed modeling, however as a result of very small sample sizes (n=149 versus n=24 versus n=14 for the three clusters I am comparing) power problems occur. That is why I am looking for an alternative approach  and thought of canonical correlations.

[Ryan]

Your sample size is a serious limiting factor with respect to any formal statistical test you plan on conducting.

You ought to tell us more about what exactly what want answered come to think of it.

I initially assumed you wanted to conduct a formal statistical test on the equality of correlation matrices [comprising the same variables, of course] from three independent samples. Is that correct? If yes, my suggestion of parameterizing a linear mixed model to perform this test may not be exactly as you might expect. Structural equation modeling would come in handy for this situation as well. Those are just two approaches that immediately come to mind, both of which require decent sample sizes.

Ryan

On Mon, Oct 12, 2015 at 8:27 AM, MaaikeSmits <[hidden email]> wrote:

Thank you Ryan for your response. I should add that I tried comparing the
clusters by means of mixed modeling, however as a result of very small
sample sizes (n=149 versus n=24 versus n=14 for the three clusters I am
comparing) power problems occur. That is why I am looking for an alternative
approach  and thought of canonical correlations.



--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/Nonlinear-Canonical-Correlation-Analysis-tp5730762p5730764.html

Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

[Art Kendall]

If you have 1 grouping variable and a set of continuous variables, and if your question is how are the groups different (how can i discriminate, in the old sense of the word, among the groups),
it sounds like a discriminant function analysis.

using the classification phase of a DISCRIMINANT helps you get some insight into the stability of the solution.

[MaaikeSmits]

To elaborate on the issue I am studying: I performed a cluster analysis on a group of 187 person, based on their characteristics on several continuous dimensions. The 3 cluster solution proved to be the best fit. I compared the clusters with GLM on the clustering variables (input variables to the cluster analysis) and also performed a discriminant analyses on these inputdimensions, which indeed confirmed the stability f the solution. Differential loadings of the inputdimension to 2 discriminant functions were apparant, and helpfull in interpretating how the clusters differentiated based on the input variables.

However, now I want to 'validate' the clusters by comparing them on relevant external measures, all of which continuous variables. I started again by comparing the clusters with GLM, however sample sizes result in power problems (n=149, n=24, n=14), hence I am looking for an alternative manner to study cluster differences on these measures. With canonical correlation I was hoping to be able to study differential relatedness of the distinct valdidation measures with clustermembership (which is one categorical variable with 3 levels). I also again tried the discriminate analyses, now performed on the external validity measures - however what confuses me - noth with OVERALS nonlineair canonical correlatin analyses as with discriminant function analysis - is that the loadings of the validation measures on the discriminant functions/variates are shown, but I can't sort out what this means for how the validation measures 'load' on the clusters itself. In other words, which of the validation measures is relativly more distinctive between the clusters.

As is probably apparent: I am not really well trained in these analyses, so pardon my probably partly incorrect use of some of the terms...

[Art Kendall]

The classification phase of a DISCRIMINANT with the cluster number as the grouping variable and variables that were uses to create the clusters as the continuous variables speaks to the quality and meaning of the clustering.

Another perspective is using the cluster membership as the grouping variable and external variables as the set of continuous set. One output you get is the univariate ANOVA for each of the continous variables.  Another output is the loadings of the continuous variables on the artificial dimension created by the DFA.

If you are   just learning DFA, ask for all of the output options and see which you can make sense of. Do theis with both DFAs, i.e., with the variables used in the clustering and the external variables.

[MaaikeSmits]

I am working on the option of discriminant analysis.
Parallel I am wondering if there is a way to get K-means clustering procedure to produce dimensional distance scores for each case to each cluster mean.  K-means now produces distance to cluster mean of the cluster it is assigned to and clustermembership but no dimensional scores on the other clusters. I can't find this as an option in drop down menus but maybe syntax offers a solution?

Having these dimensional scores would offer a possibility to compute canonical correlations with the validation measures.

[Kirill Orlov]

-->wondering if there is a way to get K-means clustering
procedure to produce dimensional distance scores for each case to each
cluster mean

No, K-means procedure in SPSS won't show distances to the alien cluster centres.
It is possible in Discriminant. It is also very simple to program the computation by syntax oneself.

If instead of the case-variables data you have matrix of euclidean distances between the cases then you can compute those same distances using function !dtocfrd (see "Matrix - End matrix functions" on my page http://www.spsstools.net/en/KO-spssmacros)

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD