How to interpret Homogeneity of Slopes Test?

[Milena Stefanovic]

Hello again,

For Homogeneity of Slopes Test, geomorph gives me fallowing report:

Call:

procD.allometry(f1 = Shape ~ cs, f2 = ~Population * Sex, logsz = TRUE, iter = 999, RRPP = TRUE, data = gdfTaxus3) 

Homogeneity of Slopes Test

                   Df   SSE       SS       R2      F      Z Pr(>F)  

Common Allometry  463 2.662                                         

Group Allometries 458 2.565 0.096938 0.031461 3.4618 3.0766   0.01 *

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The null hypothesis of parallel slopes is rejected

  based on a signficance criteron of alpha = 0.05 

Based on the results of this test, the following ANOVA table is most appropriate

Type I (Sequential) Sums of Squares and Cross-products

Randomized Residual Permutation Procedure Used

1000 Permutations

                          Df      SS       MS      Rsq       F       Z Pr(>F)   

log(size)                  1 0.18203 0.182032 0.059078 32.5029 16.5257  0.001 **

Population                 2 0.18808 0.094040 0.061041 16.7914 11.5202  0.001 **

Sex                        1 0.02398 0.023976 0.007781  4.2810  2.8459  0.021 * 

Population:Sex             2 0.02516 0.012579 0.008165  2.2461  1.8671  0.055 . 

log(size):Population       2 0.05800 0.028998 0.018823  5.1778  3.9212  0.005 **

log(size):Sex              1 0.00807 0.008069 0.002619  1.4408  1.0377  0.194   

log(size):Population:Sex   2 0.03087 0.015436 0.010020  2.7563  2.2592  0.032 * 

Residuals                458 2.56503 0.005600                                   

Total                    469 3.08121                                            

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

It is not clear to me how to interpret these results. The null hypothesis of parallel slopes is rejected, what does it mean?

Thank you in advance,

Milena

[Adams, Dean [EEOBS]]

Rejection of homogeneity of slopes means that the slope for at least one group differs from the rest. In your case, you are examining allometry. Thus, at least one group displays a differing pattern of allometry: the shape to size relationship is not the same as in other groups.

 

Now, it may be that multiple groups differ from one another, not just one.  To determine this, use advanced.procD.lm and perform the slope comparison test (see help file for an explicit example).

 

Dean

 

Dr. Dean C. Adams

Professor

Department of Ecology, Evolution, and Organismal Biology

       Department of Statistics

Iowa State University

www.public.iastate.edu/~dcadams/

phone: 515-294-3834

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[Milena Stefanovic]

Dr. Adams,

I am little confused about right model for examining patter of allometry between Population*Sex groups:

 

gdfTaxusA <- geomorph.data.frame(Shape = Y.gpa2$coords, logcs = log(Y.gpa2$Csize), Population = classifier$Population, Sex = classifier$Sex)

 

myresults5 <- advanced.procD.lm(Shape ~ logcs + Population * Sex,

                                                  ~ logcs + Population + Sex,

                                                     groups = ~ Population*Sex, slope = ~logcs, iter = 1000, data = gdfTaxusA)

 

OR:

 

myresults6 <- advanced.procD.lm(Shape ~ logcs + Population * Sex,

                                                  ~ logcs + Population * Sex,

                                                     groups = ~ Population*Sex, slope = ~logcs, iter = 1000, data = gdfTaxusA)

 

And second, should the reports for amount of shape change (contrast in slope vector length) and direction of shape change (correlations between slope vectors) be consistent with plot of PC1 of predicted values (from regression shape on size) vs log centroid size (Homogeneity of slopes_PredLine)? 

 

 

Thank you,

Milena

[Adams, Dean [EEOBS]]

Milena,

 

Neither of these models compares slopes among groups. What you need is a model with individual slopes to a model with a common slope. For ‘size’ and ‘group’ that is:

 

Y~size*group    

Y~size+group

 

Note that the first model is fully written as: Y~size+group+size:group. The size:group term contains the individual slopes.

 

For your system it seems you should have:

 

Shape ~ logcs * Population * Sex

Shape ~ logcs + Population * Sex

 

Note the ‘*’ and ‘+’ with respect to size and the groups. This determines whether the individual slope terms are present or not.

 

Dean

 

Dr. Dean C. Adams

Professor

Department of Ecology, Evolution, and Organismal Biology

       Department of Statistics

Iowa State University

www.public.iastate.edu/~dcadams/

phone: 515-294-3834

 

From: geomorph-...@googlegroups.com [mailto:geomorph-...@googlegroups.com] On Behalf Of Milena Stefanovic

Sent: Thursday, November 3, 2016 8:02 AM
To: geomorph R package <geomorph-...@googlegroups.com>

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