p-value for PLS regression model & parameter estimates?

Discussion:

(too old to reply)

Heidi

2009-09-13 07:05:21 UTC

Hi there,

I have carried out PLS (Partial Least Square) procedures and couldn't
find the p-values for the PLS model and its predictor variables from
the SPSS output. What should I do next to confirm if my results are
significant (i.e. whether the overall model as well as which
predictors are significant contributors).

Many thanks.
Heidi

Frank

2009-09-13 17:08:11 UTC

Permalink

Post by Heidi
Hi there,
I have carried out PLS (Partial Least Square) procedures and couldn't
find the p-values for the PLS model and its predictor variables from
the SPSS output. What should I do next to confirm if my results are
significant (i.e. whether the overall model as well as which
predictors are significant contributors).
Many thanks.
Heidi

The PLS Extension Module is dependent upon Python software -----
Frank

JKPeck

2009-09-14 01:47:03 UTC

Permalink

The PLS Extension Module is dependent upon Python software -----
Frank

Perhaps I should clarify things a bit.
First, the PLS extension command is implemented in Python, but it was
written by SPSS staff using the Python language and the excellent
scientific libraries, numpy and scipy, which provided the numerical
linear algebra operations. (I wrote the original version, and another
staff member generalized it to handle multiple dependent variables and
do some charts.) So the features of PLS don't have anything
particular to do with Python.

Second, the PLS algorithm doesn't really provide the kind of
significance testing you get with ordinary regression models. One
clue is that you can run PLS with more independent variables than you
have cases. It's akin to principal components except that both the
y's and the X's are projected.

HTH,
Jon Peck

Heidi

2009-09-14 14:14:09 UTC

Permalink

Post by JKPeck

The PLS Extension Module is dependent upon Python software -----
Frank

Perhaps I should clarify things a bit.
First, the PLS extension command is implemented in Python, but it was
written by SPSS staff using the Python language and the excellent
scientific libraries, numpy and scipy, which provided the numerical
linear algebra operations. (I wrote the original version, and another
staff member generalized it to handle multiple dependent variables and
do some charts.) So the features of PLS don't have anything
particular to do with Python.
Second, the PLS algorithm doesn't really provide the kind of
significance testing you get with ordinary regression models. One
clue is that you can run PLS with more independent variables than you
have cases. It's akin to principal components except that both the
y's and the X's are projected.
HTH,
Jon Peck

Thanks, Jon. I'm honoured to have my question answered by PLS
extention creator. My sample size is 38 and I also included
interaction effects in the model. Reading other scholars' works that
use PLS methodology, I wonder how they derived p-values for both the
latent factors as well as parameter estimates of independent
variables. Pls advise what further analysis to take.

Otherwise I need some benchmark(?) to decide which independent
variables, by looking at their weights, are significant contributor to
particular latent factor. On top of that, I should be able to select
number of latent factors based on cumulative X variance & cum. Y
variance. Is it sensible to make conclusion based on subjective
judgement?

It would be of great help if anyone here could show me how to write
the PLS results, i.e. what statistics to include.

Many thanks,
Heidi

Bruce Weaver

2009-09-14 17:58:28 UTC

Permalink

Post by Heidi

Post by JKPeck

The PLS Extension Module is dependent upon Python software -----
Frank

Perhaps I should clarify things a bit.
First, the PLS extension command is implemented in Python, but it was
written by SPSS staff using the Python language and the excellent
scientific libraries, numpy and scipy, which provided the numerical
linear algebra operations. (I wrote the original version, and another
staff member generalized it to handle multiple dependent variables and
do some charts.) So the features of PLS don't have anything
particular to do with Python.
Second, the PLS algorithm doesn't really provide the kind of
significance testing you get with ordinary regression models. One
clue is that you can run PLS with more independent variables than you
have cases. It's akin to principal components except that both the
y's and the X's are projected.
HTH,
Jon Peck

Thanks, Jon. I'm honoured to have my question answered by PLS
extention creator. My sample size is 38 and I also included
interaction effects in the model. Reading other scholars' works that
use PLS methodology, I wonder how they derived p-values for both the
latent factors as well as parameter estimates of independent
variables. Pls advise what further analysis to take.
Otherwise I need some benchmark(?) to decide which independent
variables, by looking at their weights, are significant contributor to
particular latent factor. On top of that, I should be able to select
number of latent factors based on cumulative X variance & cum. Y
variance. Is it sensible to make conclusion based on subjective
judgement?
It would be of great help if anyone here could show me how to write
the PLS results, i.e. what statistics to include.
Many thanks,
Heidi

I have no expertise in PLS to share with you, but I see that David
Garson has some notes on it (including some stuff about SPSS output),
and his stuff is usually very good.

http://faculty.chass.ncsu.edu/garson/PA765/pls.htm

--
Bruce Weaver
***@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/Home
"When all else fails, RTFM."

Heidi

2009-09-15 10:08:51 UTC

Permalink

Post by Bruce Weaver

Post by Heidi

Post by JKPeck

The PLS Extension Module is dependent upon Python software -----
Frank

Perhaps I should clarify things a bit.
First, the PLS extension command is implemented in Python, but it was
written by SPSS staff using the Python language and the excellent
scientific libraries, numpy and scipy, which provided the numerical
linear algebra operations. (I wrote the original version, and another
staff member generalized it to handle multiple dependent variables and
do some charts.) So the features of PLS don't have anything
particular to do with Python.
Second, the PLS algorithm doesn't really provide the kind of
significance testing you get with ordinary regression models. One
clue is that you can run PLS with more independent variables than you
have cases. It's akin to principal components except that both the
y's and the X's are projected.
HTH,
Jon Peck

Thanks, Jon. I'm honoured to have my question answered by PLS
extention creator. My sample size is 38 and I also included
interaction effects in the model. Reading other scholars' works that
use PLS methodology, I wonder how they derived p-values for both the
latent factors as well as parameter estimates of independent
variables. Pls advise what further analysis to take.
Otherwise I need some benchmark(?) to decide which independent
variables, by looking at their weights, are significant contributor to
particular latent factor. On top of that, I should be able to select
number of latent factors based on cumulative X variance & cum. Y
variance. Is it sensible to make conclusion based on subjective
judgement?
It would be of great help if anyone here could show me how to write
the PLS results, i.e. what statistics to include.
Many thanks,
Heidi

I have no expertise in PLS to share with you, but I see that David
Garson has some notes on it (including some stuff about SPSS output),
and his stuff is usually very good.
http://faculty.chass.ncsu.edu/garson/PA765/pls.htm
--
Bruce Weaver
"When all else fails, RTFM."- Hide quoted text -
- Show quoted text -

Thanks, Bruce. In fact, I depend entirely on his note to perform PLS.
Anyway, thanks again.

Heidi

thebluecliffrecord

2009-09-15 13:18:55 UTC

Permalink

Post by Heidi
I have carried out PLS (Partial Least Square) procedures and couldn't
find the p-values for the PLS model and its predictor variables from
the SPSS output. What should I do next to confirm if my results are
significant (i.e. whether the overall model as well as which
predictors are significant contributors).

Dear Heidi,

PLS provides a p-value for the statistical significance of the
"overall" model. However, PLS can not provide p-values for
"individual" predictors because the extracted PCs are linear
"combinations" of all the predictors and the responses, therefore
there can't be p-values for the individual predictors. PLS extracts
the principal components (PCs) from all raw predictors, the PCs from
the multiple responses, and then those two sets of PCs are modified to
predict the responses ( I believe you already know of this).

Post by Heidi
Otherwise I need some benchmark(?) to decide which independent
variables, by looking at their weights, are significant contributor to
particular latent factor. On top of that, I should be able to select
number of latent factors based on cumulative X variance & cum. Y
variance. Is it sensible to make conclusion based on subjective
judgement?

The loadings of the individual predictors will provide clues for the
contributions of each predictors. Check the cross-validation to
determine whther the selected number of latent factors overfilts or
not. These are mere suggestions because there are many other things
to consider. For example, the signs of the PLS regression
coefficients ("wrong" sings in regression).

I prefer not to use the term "significant" because it usually
indicates "statistical" significance.

Personally, I perform PCA and PCR before I apply the PLS because I
would like to understand the data first (with and without Y in PCA and
PCR) and PCA will give us clues the "true" dimensions of the X
(orthogonal predictors) and thus the set of predictors to be included
in multiple linear regression.

More importantly, subject knowledge should guide what predictors
should be included before applying "ANY" orthogonal transformations
such as PCR, PLS, and ridge regression. They will extract PCs no
matter what kind of data (good or bad)!

Most importantly, as you are already aware of, if predictors are
collinear, the interpretation of individual predictors is often
unwarrented ("multicollinearity"). PCR and PLS are mere mathmatical
transformation (again, no matter what kind of data!) and therefore the
interpretation of each predictors are unwarrented also, but the
extracted components could provide some clues for interpretation
"hopely".

In other words, if you already know which predictors are related, why
not use such knowledge (you come up with your own model structure)
rather than PCR and PLS.

By the way, I don't have access to SPSS but use MINITAB.

Hope this helps.

Sangdon Lee, Ph.D.,
GM Warren Tech. Center.

a***@gmail.com

2013-03-20 01:58:02 UTC

Permalink

Dear group members,

I am very happy to see that people can actually progress in their work and get few advices online to use SPSS effectively!

I am Yafaa sofia Ahres, currently working on a Project for my MSc. I have to use SPSS and the PLS Regression too. I would like to get few advices and guidelines as I never used this before. I have the Julie Pallant's Book ''SPSS Survival Manual'' it's a huge help, I know how to do many things on SPSS now thanks to her; but unfortunately there's no chapter for PLS Regression ... Therefore, if anyone can share his/her knowledge and expertise that will be great.

I am basically following the Framework/ Research Methodology of Reinartz et al. (2004; see article below via Web-link ===>

http://www.management.imu.unibe.ch/content/e6586/e6643/e6586/e6643/e6647/2004-12-21_krafft.pdf

• A dependent variable is named ‘’objective performance’’; its value is 0.045, which represents the average return on asset of the years 2011 and 2012. I tried to enter its value (0.045) into ‘’Variable View’’ and precisely ‘’Values’’, but for some reason 0.045 is changed to 0.

⇒ Could you please advise me on how to enter this variable with its correct value and measure?

• Another issue is that, when I obtained few tables corresponded to ‘’Descriptive Statistics’’, Pearson etc., all the items (statement part of my questionnaire) and variables entered in SPSS ‘’Variable View’’ were included and listed in these tables.

⇒ I would like to know how to obtain the tables but with only the construct and not all the items that form the construct/scale (like in the summary statistics for the measurement scales in Reinartz et al 2004 journal article shared in this email) for:
- Descriptive Statistics (with Mean, Standard deviation. Minimum, Maximum etc.)
- Cronbach Alpha for Reliability Analysis.
- Pearson correlation and Spearman correlation.

• PLS:
After downloading the extension module (which was not really easy), I am trying to run PLS in SPSS considering the Equation (1), the Model 1 & 2 (see above and/or article provided) and the standardised PLS coefficients (provided by the authors for the construct model).

⇒ If you could give me some guidelines to run PLS correctly that will be fantastic; I have tried many times and no success...

• Equation (1):
(1) Economic performance =
α +
+ β1 relationship initiation
+ β2 relationship maintenance
+ β3 relationship termination
+ β4 CRM-compatible organizational alignment
+ β5 CRM technology
+ γ1 (CRM-compatible organizational alignment x relationship initiation) 
+ γ2 (CRM-compatible organizational alignment x relationship maintenance)
+ γ3 (CRM-compatible organizational alignment x relationship termination)
+ γ4 (CRM technology x relationship initiation) 
+ γ5 (CRM technology x relationship maintenance)
+ γ6 (CRM technology x relationship termination)
+ σ1 Investment banks 1
+ σ2 Investment banks 2
+ σ3 Investment banks 3
+ σ4 Investment banks 4

Variables are grouped into:
• Main effects (β)
• Interaction effect (γ)
• Control variables (σ)
Formative multi-item measures:
• Relationship initiation, maintenance, relationship termination
• CRM-compatible organizational alignment
• CRM technology.

Subject to the economic performance (both objective and perceptual) we obtain two different models:
• MODEL 1: Economic performance (perceptual)= f(covariates
• MODEL 2: Economic Performance (objective)= f(covariates

• Standardised PLS coefficients:

INITIATE =
.389 X IMEASURE + .379 X ACQUISIT + .375 X REGAINTRUST

MAINTAIN =
.283 X MMEASURE + .340 X RETAIN + .388 X CROSS_UP + .267 X REFERRAL

TERMINATE =
.367 X TMEASURE + .759 X EXIT

• The Survival Book does not explain how to run ''Square roots of Average Variance Extracted (AVE) in the diagonal''; I am currently trying to find it out via blogs, YouTube etc. If anyone could share the steps to obtain AVE that will be nice.

• Histograms, Bar Graphs, Boxplot, Line Graphs, Scatterplots etc. are easy to obtain, but for how can I select several variables at the same time.
⇒ I would like to know how I could obtain the general construct instead of every single variable that form the he construct/scale.

• I plan to use the Spearman rho and/or Pearson correlation for the Correlation Analysis; however, the Journal article provided above does not include this correlation analysis.

⇒ Therefore, I would like to know if it is worthwhile to conduct a Correlation Analysis utilising Pearson, Spearman rho. In my opinion, it is as it allows to determining the direction of the relationship between the variables, and the strength of the relationship; but also calculating the coefficient of determination and assessing the significance level.

Many thanks, any assistance would be greatly appreciated.

Exchange via Emails might be better, especially for sharing files because I cannot see a link to attached files in this Google Group Page.

***@gmail.com

Many thanks again!