Growth difference

Growth matrix and growth difference matrix based inference based on Lele and Richtsmeier (1992, 1995).

Usage

edma_gm(a1, a2, ...)
get_gm(object, ...)
# S3 method for edma_gm
get_gm(object, sort=FALSE, level=0.95,
    what="all", ...)

edma_gdm(a1, a2, b1, b2, ...)
get_gdm(object, ...)
# S3 method for edma_gdm
get_gdm(object, sort=FALSE, level=0.95,
    what="all", ...)

# S3 method for edma_gm
print(x, ...)
# S3 method for edma_gdm
print(x, ...)
# S3 method for edma_gm
global_test(object, ...)
# S3 method for edma_gdm
global_test(object, ...)
# S3 method for edma_gdm
landmarks(x, ...)
# S3 method for edma_gdm
dimensions(x, ...)

# S3 method for edma_gdm
plot_ord(x, ...)
# S3 method for edma_gdm
plot_clust(x, ...)

Arguments

a1, a2, b1, b2

EDMA fit object to compare growths.

x, object

an EDMA GM or GDM objects.

sort

logical, if stacked distances are to be sorted, see Examples.

level

numeric, between 0 and 1, alpha level for confidence interval.

what

what part of the ford differences to return: "all", "less" or "greater" than 1, "signif" or "nonsignif".

...

other arguments passed to edma_fdm, like ref_denom.

Details

Growth matrix (GM) is calculated as the ratio of form matrices (FM) from the numerator and denominator objects following Lele and Richtsmeier (1992, 1995): GM(A1,A2) = FM(A2)/FM(A1). Form matrices are formed as pairwise Euclidean distances between landmarks from EDMA fit objects using the estimated mean forms.

Growth difference matrix (GDM) is calculated as GDM(A1,A2,B1,B2) = GM(B1,B2) / GM(A1,A2).

Inference and visualization is similar to how it is done for FDMs.

Value

edma_gm compares two EDMA fit objects and calculates GM.

edma_gdm compares 4 EDMA fit objects and calculates GDM.

The plot_ord and plot_clust

produce plots based on dissimilarities among specimens in the 2 or 4 objects (for GM and GDM, respectively).

References

Lele, S. R., and Richtsmeier, J. T., 1992. On comparing biological shapes: detection of influential landmarks. American Journal of Physical Anthropology 87:49--65. <doi:10.1002/ajpa.1330870106>

Lele, S. R., and Richtsmeier, J. T., 1995. Euclidean distance matrix analysis: confidence intervals for form and growth differences. American Journal of Physical Anthropology 98:73--86. <doi:10.1002/ajpa.1330980107>

Author

Peter Solymos, Subhash R. Lele, Theodore M. Cole, Joan T. Richtsmeier

See also

Nonparametric fit: edma_fit

Form difference: edma_fdm

Shape difference: edma_sdm

Examples

file_a1 <- system.file("extdata/growth/CZEM_wt_global.xyz",
    package="EDMAinR")
file_a2 <- system.file("extdata/growth/CZP0_wt_global.xyz",
    package="EDMAinR")

l <- c("amsph", "bas", "loci", "lpto", "lsqu",
        "lsyn", "roci", "rpto", "rsqu", "rsyn")

a1 <- read_xyz(file_a1)[l,,]
a2 <- read_xyz(file_a2)[l,,]
a1
#> EDMA data: Crouzon unaffected embryonic mouse
#> 10 landmarks, 3 dimensions, 31 specimens
a2
#> EDMA data: Crouzon unaffected newborn mouse
#> 10 landmarks, 3 dimensions, 11 specimens

fit_a1 <- edma_fit(a1, B=10)
fit_a2 <- edma_fit(a2, B=10)

## --- growth matrix ---

gm <- edma_gm(a1=fit_a1, a2=fit_a2, B=10)
gm
#> EDMA growth matrix
#> Call: edma_gm(a1 = fit_a1, a2 = fit_a2, B = 10)
#> 10 bootstrap runs (ref: denominator)
#> Tobs = 1.259, p < 2.22e-16
global_test(gm)
#> 
#> 	Bootstrap based EDMA G-test
#> 
#> data:  growth matrix
#> G -value = 1.259, B = 10, p-value < 2.2e-16
#> 
head(confint(gm))
#>                2.5%    97.5%
#> bas-amsph  1.098286 1.129447
#> loci-amsph 1.087711 1.122313
#> lpto-amsph 1.129613 1.154855
#> lsqu-amsph 1.128924 1.180152
#> lsyn-amsph 1.117893 1.150160
#> roci-amsph 1.086130 1.121514
head(get_gm(gm))
#>    row   col     dist    lower    upper
#> 1  bas amsph 1.116726 1.098286 1.129447
#> 2 loci amsph 1.112833 1.087711 1.122313
#> 3 lpto amsph 1.144189 1.129613 1.154855
#> 4 lsqu amsph 1.149705 1.128924 1.180152
#> 5 lsyn amsph 1.139680 1.117893 1.150160
#> 6 roci amsph 1.110515 1.086130 1.121514
head(get_gm(gm, sort=TRUE, decreasing=TRUE))
#>     row  col     dist    lower    upper
#> 45 rsyn rsqu 1.196344 1.175489 1.217173
#> 31 lsyn lsqu 1.194661 1.166476 1.219401
#> 41 rsqu roci 1.159037 1.137300 1.166941
#> 35 rsyn lsqu 1.155865 1.133920 1.178853
#> 19 lsqu loci 1.155629 1.134197 1.162690
#> 16 rsqu  bas 1.155440 1.143204 1.167108
head(get_gm(gm, sort=TRUE, decreasing=FALSE))
#>     row  col      dist     lower    upper
#> 28 rpto lpto 0.9502249 0.9103352 1.001992
#> 34 rsqu lsqu 1.0364970 1.0230670 1.050673
#> 21 roci loci 1.0365211 1.0108008 1.048766
#> 27 roci lpto 1.0423805 1.0279959 1.061963
#> 22 rpto loci 1.0515532 1.0313671 1.065774
#> 29 rsqu lpto 1.0610708 1.0500582 1.070469

plot_ord(gm)

plot_clust(gm)

plot_test(gm)

plot_ci(gm)

plot_2d(gm)

if (interactive())
    plot_3d(gm)

## --- growth difference matrix ---

file_b1 <- system.file("extdata/growth/CZEM_mut_global.xyz",
    package="EDMAinR")
file_b2 <- system.file("extdata/growth/CZP0_mut_global.xyz",
    package="EDMAinR")

b1 <- read_xyz(file_b1)[l,,]
b2 <- read_xyz(file_b2)[l,,]
b1
#> EDMA data: Crouzon mutant embryonic mouse
#> 10 landmarks, 3 dimensions, 18 specimens
b2
#> EDMA data: Crouzon mutant newborn mouse
#> 10 landmarks, 3 dimensions, 11 specimens

fit_b1 <- edma_fit(b1, B=10)
fit_b2 <- edma_fit(b2, B=10)

gdm <- edma_gdm(a1=fit_a1, a2=fit_a2, b1=fit_b1, b2=fit_b2, B=10)
gdm
#> EDMA growth difference matrix
#> Call: edma_gdm(a1 = fit_a1, a2 = fit_a2, b1 = fit_b1, b2 = fit_b2, 
#>     B = 10)
#> 10 bootstrap runs (ref: denominator)
#> Tobs = 1.1113, p = 0.27273
global_test(gdm)
#> 
#> 	Bootstrap based EDMA G-test
#> 
#> data:  growth difference matrix
#> G -value = 1.1113, B = 11, p-value = 0.2727
#> 
head(confint(gdm))
#>                 2.5%     97.5%
#> bas-amsph  0.9915716 1.0368321
#> loci-amsph 0.9781170 1.0257089
#> lpto-amsph 0.9774645 1.0097597
#> lsqu-amsph 0.9748169 0.9997238
#> lsyn-amsph 0.9864931 1.0313089
#> roci-amsph 0.9747043 1.0231884
head(get_gdm(gdm))
#>    row   col      dist     lower     upper
#> 1  bas amsph 0.9871097 0.9915716 1.0368321
#> 2 loci amsph 0.9962675 0.9781170 1.0257089
#> 3 lpto amsph 0.9935320 0.9774645 1.0097597
#> 4 lsqu amsph 1.0057657 0.9748169 0.9997238
#> 5 lsyn amsph 0.9844980 0.9864931 1.0313089
#> 6 roci amsph 0.9981683 0.9747043 1.0231884
head(get_gdm(gdm, sort=TRUE, decreasing=TRUE))
#>     row   col     dist     lower     upper
#> 39 rsyn  lsyn 1.040292 0.9078684 0.9896739
#> 18 lpto  loci 1.013272 0.9446575 1.0240004
#> 40 rpto  roci 1.010858 0.9487873 0.9977089
#> 36 roci  lsyn 1.010448 0.9596945 1.0071426
#> 21 roci  loci 1.008071 0.9443650 1.0318483
#> 9  rsyn amsph 1.007449 0.9596942 1.0107837
head(get_gdm(gdm, sort=TRUE, decreasing=FALSE))
#>     row  col      dist     lower    upper
#> 43 rsqu rpto 0.9361207 1.0303048 1.067071
#> 25 lsqu lpto 0.9485414 1.0157609 1.077698
#> 29 rsqu lpto 0.9569724 1.0006861 1.067052
#> 33 rpto lsqu 0.9666629 0.9913131 1.051787
#> 41 rsqu roci 0.9766552 0.9979848 1.039299
#> 19 lsqu loci 0.9791661 0.9953173 1.036952

plot_ord(gdm)

plot_clust(gdm)

plot_test(gdm)

plot_ci(gdm)

plot_2d(gdm) # need real data

if (interactive())
    plot_3d(gdm)