date:20160405

Re: [MORPHMET] replacing df with principal components for MANOVA tests

2016-04-05 Thread Collyer, Michael

Apology for the confusion.  I had intended that one could use randomization 
tests for Procrustes residuals rather than obtaining PC scores, and various 
functions in R will allow this, even if the number of shape variables exceeds 
the number of subjects.

I just checked, and prcomp will naturally reduce the dimensions of the $x 
matrix if the number of variables exceeds the number of subjects to be the 
lesser of the number of variables or n-1, where n is the number of subjects.  
(Note: it might return n PCs instead of n-1, but the PC scores are effectively 
0 in the last PC.)  It will not, however, reduce the number of dimensions 
because of e.g., invariance in scale, orientation, or location of the landmark 
configurations, following GPA.  If one were to convert Procrustes residuals to 
PC scores, and not remove excess PCs, the manova function in R will treat these 
as credible variables even though the number of variables exceeds the actual 
dimensionality of the data space.  If one performs a procedure as follows:

Y <- prcomp(my.Procrustes.residuals)$x
summary(manova(Y ~ x1 + x2 + …))

The manova function has no mechanism for correcting for the extra Y dimensions. 
 It will either blow up (best case scenario) or tack on extra df in the summary 
(even worse).  (The determinant of crossprod(Y) should be close 0, which should 
arrest the function, but I’m not sure about the manova traps.)  However, if one 
does this:

PCA <- prcomp(my.Procrustes.residuals)
Y <- PCA$x[, zapsmall(PCA$sdev) > 0]
summary(manova(Y ~ x1 + x2 + …))

The number of columns in Y will be the lesser of n-1 or the number of 
Procrustes residuals times the dimensions used for the landmarks, minus the 
invariant dimensions (because of scaling, orientation, and centering, and maybe 
use of semilandmarks).  This will not alleviate the issues Dr. Rohlf pointed 
out.  In fact, the manova.summary function will return an error if the number 
of columns of Y exceeds the error degrees of freedom for the model used.  Thus, 
if prcomp is being used simply because the number of variables exceeds the 
number of research subjects, problems will likely persist with the parametric 
approach.

By “culling the dimensions” I was referring to removing the superfluous PCs, 
specifically when using prcomp to do PCA  (as it won’t), not advocating any 
chicanery for manipulating MANOVA.

Mike

Michael Collyer

Associate Professor
Biostatistics
Department of Biology
Western Kentucky University
1906 College Heights Blvd. #11080
Bowling Green, KY 42101-1080
Phone: 270-745-8765; Fax: 270-745-6856
Email: michael.coll...@wku.edu

On Apr 5, 2016, at 1:15 PM, F. James Rohlf 
> wrote:

Note: to give statistically reliable results it needs to do more than just 
“culls the dimensions of x to match the number of positive non-zero 
eigenvalues”. You need to have the number of degrees of freedom much larger 
than the number of dimensions of the space or else you are likely to find that 
the PC dimensions with the smallest eigenvalues apparently account for most of 
the differences among groups. Simply using randomization tests do not solve 
this problem.


F. James Rohlf, Distinguished Professor, Emeritus. Ecology & Evolution
Research Professor, Anthropology
Stony Brook University

From: Collyer, Michael [mailto:michael.coll...@wku.edu]
Sent: Tuesday, April 5, 2016 5:29 AM
To: Brenna Hays >
Cc: MORPHMET >
Subject: Re: [MORPHMET] replacing df with principal components for MANOVA tests

Brenna,

The PCA you performed produces a list of objects, one of which is a matrix of 
PC scores.

Change AIS.PC to AISPC$x, and it should work.  In this case, $x is the matrix 
of scores.

The help files for the functions you use tell you the objects that are 
returned.  You can also use attributes() to see the list of objects returned.  
The $ indicate that you are going to the list and extracting the object that 
follows.

Just as a cautionary note, you might make sure that the number of columns for x 
is not the same as the number of landmarks times the dimensions (2 or 3).  I 
cannot remember if R automatically culls the dimensions of x to match the 
number of positive non-zero eigenvalues.  If not, you might have to do that 
yourself.  There are also non-parametric MANOVA options that do not rely on 
degrees of freedom, which would make theses steps unnecessary, if you are 
comfortable with using randomization tests.

Good luck!
Mike

Michael Collyer

Associate Professor
Biostatistics
Department of Biology
Western Kentucky University
1906 College Heights Blvd. #11080
Bowling Green, KY 42101-1080
Phone: 270-745-8765; Fax: 270-745-6856
Email: michael.coll...@wku.edu

On Apr 5, 2016, at 10:16 AM, Brenna

RE: [MORPHMET] replacing df with principal components for MANOVA tests

2016-04-05 Thread F. James Rohlf

Note: to give statistically reliable results it needs to do more than just 
“culls the dimensions of x to match the number of positive non-zero 
eigenvalues”. You need to have the number of degrees of freedom much larger 
than the number of dimensions of the space or else you are likely to find that 
the PC dimensions with the smallest eigenvalues apparently account for most of 
the differences among groups. Simply using randomization tests do not solve 
this problem.

 



F. James Rohlf, Distinguished Professor, Emeritus. Ecology & Evolution

Research Professor, Anthropology

Stony Brook University

 

From: Collyer, Michael [mailto:michael.coll...@wku.edu] 
Sent: Tuesday, April 5, 2016 5:29 AM
To: Brenna Hays 
Cc: MORPHMET 
Subject: Re: [MORPHMET] replacing df with principal components for MANOVA tests

 

Brenna, 

 

The PCA you performed produces a list of objects, one of which is a matrix of 
PC scores.

 

Change AIS.PC to AISPC$x, and it should work.  In this case, $x is the matrix 
of scores.

 

The help files for the functions you use tell you the objects that are 
returned.  You can also use attributes() to see the list of objects returned.  
The $ indicate that you are going to the list and extracting the object that 
follows.  

 

Just as a cautionary note, you might make sure that the number of columns for x 
is not the same as the number of landmarks times the dimensions (2 or 3).  I 
cannot remember if R automatically culls the dimensions of x to match the 
number of positive non-zero eigenvalues.  If not, you might have to do that 
yourself.  There are also non-parametric MANOVA options that do not rely on 
degrees of freedom, which would make theses steps unnecessary, if you are 
comfortable with using randomization tests.

 

Good luck!

Mike

 

Michael Collyer

Associate Professor

Biostatistics
Department of Biology
Western Kentucky University
1906 College Heights Blvd. #11080 
Bowling Green, KY 42101-1080
Phone: 270-745-8765; Fax: 270-745-6856
Email: michael.coll...@wku.edu  

 

On Apr 5, 2016, at 10:16 AM, Brenna Hays  > wrote:

 

I have been reading up on MANOVA and come across the common complication 
requiring a large number of degrees of freedom. After performing Procrustes 
superimpositions on my landmark configurations, along with my small sample 
sizes, is not allowing me to perform MANOVA tests. 

 

I have read that one can fix this problem by replacing the coordinates with 
principal components. The coding from my information source is very vague, but 
I've been trying some different things. Below is my code - note the error 
message at the bottom. 

 

AISarray <- two.d.array(AIS.shape)

 

ID <- c(1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3)

Depth <- c(3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5)

Region <- c(7, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5)

RR <- c(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2)

CDR <- c(2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)

 

AISdf <- cbind(AISarray, ID, Depth, Region, RR, CDR)

 

specs <- as.factor(AISdf[,51])

depth <- as.factor(AISdf[,52])

region <- as.factor(AISdf[,53])

rr <- as.factor(AISdf[,54])

cdr <- as.factor(AISdf[,55])

 

AIS.PC <- prcomp(AISarray)

summary(manova(lm(AIS.PC~specs*region))) #NOT WORKING

Error in model.frame.default(formula = AIS.PC ~ specs * region, 
drop.unused.levels = TRUE) : 

  invalid type (list) for variable 'AIS.PC'

 

It seems MANOVA requires a data frame, but replacing the coordinates with 
principal components turns it into a list. I cannot find any other information 
on this matter. Any help would be much appreciated. 

Thanks, 

 

Brenna Hays

Research Assistant, Master's Student

Nova Southeastern University

 

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Re: [MORPHMET] replacing df with principal components for MANOVA tests

2016-04-05 Thread Collyer, Michael

Brenna,

The PCA you performed produces a list of objects, one of which is a matrix of 
PC scores.

Change AIS.PC to AISPC$x, and it should work.  In this case, $x is the matrix 
of scores.

The help files for the functions you use tell you the objects that are 
returned.  You can also use attributes() to see the list of objects returned.  
The $ indicate that you are going to the list and extracting the object that 
follows.

Just as a cautionary note, you might make sure that the number of columns for x 
is not the same as the number of landmarks times the dimensions (2 or 3).  I 
cannot remember if R automatically culls the dimensions of x to match the 
number of positive non-zero eigenvalues.  If not, you might have to do that 
yourself.  There are also non-parametric MANOVA options that do not rely on 
degrees of freedom, which would make theses steps unnecessary, if you are 
comfortable with using randomization tests.

Good luck!
Mike

Michael Collyer

Associate Professor
Biostatistics
Department of Biology
Western Kentucky University
1906 College Heights Blvd. #11080
Bowling Green, KY 42101-1080
Phone: 270-745-8765; Fax: 270-745-6856
Email: michael.coll...@wku.edu

On Apr 5, 2016, at 10:16 AM, Brenna Hays 
> wrote:

I have been reading up on MANOVA and come across the common complication 
requiring a large number of degrees of freedom. After performing Procrustes 
superimpositions on my landmark configurations, along with my small sample 
sizes, is not allowing me to perform MANOVA tests.

I have read that one can fix this problem by replacing the coordinates with 
principal components. The coding from my information source is very vague, but 
I've been trying some different things. Below is my code - note the error 
message at the bottom.

AISarray <- two.d.array(AIS.shape)

ID <- c(1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3)
Depth <- c(3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5)
Region <- c(7, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5)
RR <- c(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2)
CDR <- c(2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)

AISdf <- cbind(AISarray, ID, Depth, Region, RR, CDR)

specs <- as.factor(AISdf[,51])
depth <- as.factor(AISdf[,52])
region <- as.factor(AISdf[,53])
rr <- as.factor(AISdf[,54])
cdr <- as.factor(AISdf[,55])

AIS.PC <- prcomp(AISarray)
summary(manova(lm(AIS.PC~specs*region))) #NOT WORKING
Error in model.frame.default(formula = AIS.PC ~ specs * region, 
drop.unused.levels = TRUE) :
  invalid type (list) for variable 'AIS.PC'

It seems MANOVA requires a data frame, but replacing the coordinates with 
principal components turns it into a list. I cannot find any other information 
on this matter. Any help would be much appreciated.
Thanks,

Brenna Hays
Research Assistant, Master's Student
Nova Southeastern University

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[MORPHMET] replacing df with principal components for MANOVA tests

2016-04-05 Thread Brenna Hays

I have been reading up on MANOVA and come across the common complication 
requiring a large number of degrees of freedom. After performing Procrustes 
superimpositions on my landmark configurations, along with my small sample 
sizes, is not allowing me to perform MANOVA tests.

I have read that one can fix this problem by replacing the coordinates with 
principal components. The coding from my information source is very vague, 
but I've been trying some different things. Below is my code - note the 
error message at the bottom. 

AISarray <- two.d.array(AIS.shape)

ID <- c(1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3)
Depth <- c(3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5)
Region <- c(7, 8, 8, 8, 8, 8, 8, 8, 5, 5, 5)
RR <- c(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2)
CDR <- c(2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)

AISdf <- cbind(AISarray, ID, Depth, Region, RR, CDR)

specs <- as.factor(AISdf[,51])
depth <- as.factor(AISdf[,52])
region <- as.factor(AISdf[,53])
rr <- as.factor(AISdf[,54])
cdr <- as.factor(AISdf[,55])

AIS.PC <- prcomp(AISarray)
summary(manova(lm(AIS.PC~specs*region))) #NOT WORKING
Error in model.frame.default(formula = AIS.PC ~ specs * region, 
drop.unused.levels = TRUE) : 
  invalid type (list) for variable 'AIS.PC'

It seems MANOVA requires a data frame, but replacing the coordinates with 
principal components turns it into a list. I cannot find any other 
information on this matter. Any help would be much appreciated. 
Thanks, 

Brenna Hays
Research Assistant, Master's Student
Nova Southeastern University

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[MORPHMET] Understanding the values from Procrustes ANOVA

2016-04-05 Thread Christina Berry

Hey guys,

I have performed a Procrustes ANOVA to look at the error values for my 
landmarks in MorphoJ but I don't really understand the values the results 
are giving me, the readout it:

Procrustes ANOVA: Procrustes ANOVA ...
Dataset: Porose errors 2

Classifiers used for the Procrustes ANOVA:
Individuals: ID
Error 1: Individual

Centroid size:
EffectSSMS   dfF  P (param.)
Individual   0.0361330.009033   4   1.39  0.2858
Error 1  0.0977610.006517  15 484.25  <.0001
Residual 0.0002690.13  20

Shape, Procrustes ANOVA:
EffectSS  MSdfF  P (param.)   Pillai tr.   P 
(param.)
Individual 0.052962970.0011033952   48   1.76  0.0044   
 2.67   0.
Error 10.112937960.0006274331  180  44.64  <.0001   
10.72   <.0001
Residual   0.003373360.140557  240

I guess my specific questions are what is the difference between centroid 
and shape, and do I want high or low value for the error 1 and individual? 
I need to summarize these results in my thesis but I am really not sure how 
to

All the Best

Chrissy

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Re: [MORPHMET] replacing df with principal components for MANOVA tests

RE: [MORPHMET] replacing df with principal components for MANOVA tests

Re: [MORPHMET] replacing df with principal components for MANOVA tests

[MORPHMET] replacing df with principal components for MANOVA tests

[MORPHMET] Understanding the values from Procrustes ANOVA

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