This repository provides two customized functions which can be used to visualize ultrasound tongue contours fitted using GAMM (Generalized Additive Mixed Models).
The contours are displayed in the polar coordinate system by using the scatterpolar plot type provided by plotly.
For a quick demo, first we import the example data:
df_gamm = read.csv("data_gamm_example.csv")
head(df_gamm) Subject Point Theta R V1 V2 V1.V2
1 S1 1 0.6428341 67.0793 i NR i.NR
2 S1 1 0.6428341 54.5902 a NR a.NR
3 S1 1 0.6428341 55.2726 i R i.R
4 S1 1 0.6428341 55.9623 u R u.R
5 S1 1 0.6428341 55.8445 a R a.R
6 S1 1 0.6428341 51.6170 u R u.R
Regarding our example data, each individual tongue contour consists of 42 data points.
The coulmn Theta and R represent the angular (rad) and the radial (mm) coordinate respectively.
V1 and V2 are categorical variables, and V1.V2 indicates the interaction between them.
We then fit a simple GAMM model using bam() from the package mgcv:
library(mgcv)
cols = c("Subject", "V1", "V2", "V1.V2")
df_gamm[cols] = lapply(df_gamm[cols], factor)
gamm.model = bam(R ~ V1.V2 +
s(Theta, bs="cr", k=10) +
s(Theta, bs="cr", k=10, by=V1.V2) +
s(Theta, Subject, bs="fs", k=10, m=1, by=V1),
data=df_gamm, discrete=TRUE)
summary(gamm.model)Family: gaussian
Link function: identity
Formula:
R ~ V1.V2 + s(Theta, bs = "cr", k = 10) + s(Theta, bs = "cr",
k = 10, by = V1.V2) + s(Theta, Subject, bs = "fs",
k = 10, m = 1, by = V1)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 57.78775 2.65257 21.786 <2e-16 ***
V1.V2a.R 1.00951 0.06848 14.743 <2e-16 ***
V1.V2e.NR 0.23623 3.83072 0.062 0.951
V1.V2e.R 0.63526 3.83073 0.166 0.868
V1.V2i.NR -0.52626 3.83562 -0.137 0.891
V1.V2i.R -0.28005 3.83562 -0.073 0.942
V1.V2o.NR -0.27973 3.93970 -0.071 0.943
V1.V2o.R -0.14944 3.93977 -0.038 0.970
V1.V2u.NR 0.71485 3.82624 0.187 0.852
V1.V2u.R 1.42654 3.82626 0.373 0.709
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df F p-value
s(Theta) 7.342 7.511 50.210 <2e-16 ***
s(Theta):V1.V2a.NR 7.853 8.618 39.268 <2e-16 ***
s(Theta):V1.V2a.R 1.001 1.001 1.071 0.3007
s(Theta):V1.V2e.NR 8.708 8.962 107.222 <2e-16 ***
s(Theta):V1.V2e.R 1.001 1.001 1.275 0.2589
s(Theta):V1.V2i.NR 8.227 8.798 52.590 <2e-16 ***
s(Theta):V1.V2i.R 1.001 1.002 3.078 0.0793 .
s(Theta):V1.V2o.NR 8.586 8.925 96.186 <2e-16 ***
s(Theta):V1.V2o.R 1.001 1.001 1.571 0.2099
s(Theta):V1.V2u.NR 8.491 8.907 114.562 <2e-16 ***
s(Theta):V1.V2u.R 1.001 1.002 4.123 0.0422 *
s(Theta,Subject):V1a 92.898 99.000 619.902 <2e-16 ***
s(Theta,Subject):V1e 91.495 99.000 608.968 <2e-16 ***
s(Theta,Subject):V1i 91.790 99.000 352.313 <2e-16 ***
s(Theta,Subject):V1o 83.285 89.000 342.464 <2e-16 ***
s(Theta,Subject):V1u 93.150 99.000 626.317 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Rank: 608/609
R-sq.(adj) = 0.892 Deviance explained = 89.3%
fREML = 1.1866e+05 Scale est. = 12.925 n = 43554
To be able to use the customized plotting functions, pre-install the following packages: itsadug, magrittr, plotly, and stringr.
For example, if we want to visualize the contour for the category "a.R", we simply do:
library(itsadug)
library(magrittr)
library(plotly)
library(stringr)
plot_GAMM_polar(model=gamm.model, target="V1.V2", var1="a.R", title="a.R")
If we want to compare the difference between two contours, then specify the other category in var2:
plot_GAMM_polar(model=gamm.model, target="V1.V2", var1="a.R", var2="a.NR", title="a.R & a.NR")
As shown in the image above, when two categories were specified, the shaded regions indicate the areas where two contours have significant differences.
On the other hand, if we were to show multiple contours (more than 3), use plot_GAMM_polar_multi() and specify the categories at the end:
plot_GAMM_polar_multi(model=gamm.model, target="V1.V2", title="a.R & i.R & u.R", "a.R", "i.R", "u.R")
If no category was specified, the function will show all contours:
plot_GAMM_polar_multi(model=gamm.model, target="V1.V2", title="V1.V2")