New version of the manuscript

And changes on some default parameter in multivariate.R

DESCRIPTION

@@ -24,7 +24,6 @@ Suggests: knitr,
     vegan
 VignetteBuilder: knitr
 Collate: 
-    'IR.R'
     'internals.R'
     'procmod_frame.R'
     'multivariate.R'

NAMESPACE

@@ -26,7 +26,6 @@ export(bicenter)
 export(corls)
 export(corls.partial)
 export(corls.test)
-export(icor)
 export(is.euclid)
 export(is.procmod.frame)
 export(nmds)

R/multivariate.R

@@ -62,7 +62,7 @@ as.data.frame.dist <- function(x, row.names = NULL, optional = FALSE, ...) {
 #' @author Christelle Gonindard-Melodelima
 #' @export
 nmds <- function(distances,
-                 maxit = 50, trace = TRUE,
+                 maxit = 100, trace = FALSE,
                  tol = 0.001, p = 2) {
 
 

man/nmds.Rd

@@ -4,7 +4,7 @@
 \alias{nmds}
 \title{Project a distance matrix in a euclidean space (NMDS).}
 \usage{
-nmds(distances, maxit = 50, trace = TRUE, tol = 0.001, p = 2)
+nmds(distances, maxit = 100, trace = FALSE, tol = 0.001, p = 2)
 }
 \arguments{
 \item{distances}{a \code{\link[stats]{dist}} object or a

manuscript/main.Rnw

@@ -359,7 +359,7 @@ r2s <- c(1:2) * 5/100
 n_rand <- 1000
 @
 
-To evaluate relative power of the three considered tests, pairs of to random matrices were produced for various $p \in \{\Sexpr{p_qs}\}$, $n \in \{\Sexpr{n_indivduals}\}$ and two levels of shared variances $R^2 \in \{\Sexpr{r2s}\}$. For each combination of parameters, $k = \Sexpr{n_sim}$ simulations are run. Each test are estimated based on $\Sexpr{n_rand}$ randomizations for the $CovLs$ test, or permutations for \texttt{protest} and \texttt{procuste.rtest}.
+To evaluate relative power of the three considered tests, pairs of to random matrices were produced for various $p \in \{\Sexpr{p_qs}\}$, $n \in \{\Sexpr{n_indivduals}\}$ and two levels of shared variations $R^2 \in \{\Sexpr{r2s}\}$. For each combination of parameters, $k = \Sexpr{n_sim}$ simulations are run. Each test are estimated based on $\Sexpr{n_rand}$ randomizations for the $CovLs$ test, or permutations for \texttt{protest} and \texttt{procuste.rtest}.
 
 <<estimate_power, cache=TRUE, message=FALSE, warning=FALSE, include=FALSE, dependson="estimate_power_setting">>=
 
@@ -634,10 +634,10 @@ print(tab,
 
 \subsection{Power of the test based on randomisation}
 
-Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is equivalent of the power estimated for both \texttt{vegan::protest} and \texttt{ade4::procuste.rtest} tests (Table \ref{tab:power}). As for the two other tests, power decreases when the number of variable ($p$ or $q$) increases and increase with the number of individuals and the shared variance. The advantage of the test based on the Monte-Carlo estimation of $\overline{RCovLs(X,Y)}$ is to remove the need of running a supplementary set of permutations when \irls is computed.
+Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is equivalent of the power estimated for both \texttt{vegan::protest} and \texttt{ade4::procuste.rtest} tests (Table \ref{tab:power}). As for the two other tests, power decreases when the number of variable ($p$ or $q$) increases and increase with the number of individuals and the shared variation. The advantage of the test based on the Monte-Carlo estimation of $\overline{RCovLs(X,Y)}$ is to remove the need of running a supplementary set of permutations when \irls is computed.
 
 \begin{table}[!t]
-\processtable{Power estimation of the procruste tests for two low level of shared variances $5\%$ and $10\%$.\label{tab:power}} {
+\processtable{Power estimation of the procruste tests for two low level of shared variations $5\%$ and $10\%$.\label{tab:power}} {
 <<power_table, echo=FALSE, results="asis" >>=
 n_indivduals <- dimnames(power)[[1]]
 p_qs <- dimnames(power)[[2]]
@@ -691,7 +691,8 @@ print(tab,
 }{} % <- we can add a footnote in the last curly praces
 \end{table}
 
-\subsection{Evaluating the shared variance}
+\subsection{Evaluating the shared variation}
+$\rls$ can be considered for matrices as a strict equivalent of Pearson's $\rpearson$ for vectors. Therefore its squared value is an estimator of the shared variation between two matrices. But because of over-fitting the estimation is over-estimated. The proposed corrected vection ($\irls$) of that coefficient is able to provide a good estimate of the shared variation and is perfectly robust to the over-fitting phenomenon (Figure~\ref{fig:shared_variation}). Only a small over evalution is observable for the low values of simulated shared variation.
 
 \begin{figure*}[!tpb]%figure1
 <<fig__r2, echo=FALSE, message=FALSE, warning=FALSE, fig.height=4, fig.width=8>>=
@@ -715,7 +716,7 @@ r2_sims_all %>%
   theme(axis.text.x = element_text(angle = 45, size=7, hjust = 1))
 @
 \caption{Shared variation ($R^2$) between two matrices is mesured with both the corrected ($\irls$) and the original ($\rls$) versions of the procrustean correlation coefficient. A gradiant of $R^2$ is simulated for two population sizes ($n \in \{10,24\}$) and two numbers of descriptive variables ($p \in \{10,100\}$). The black dashed line corresponds to a perfect match where measured $R^2$ equals the simulated one.}
-\label{fig:shared_variance}
+\label{fig:shared_variation}
 \end{figure*}
 
 

manuscript/main.tex

@@ -233,7 +233,7 @@ $p \in \{10, 20, 50\}$ are simulated under the null hypothesis of independancy.
 
 
 
-To evaluate relative power of the three considered tests, pairs of to random matrices were produced for various $p \in \{10, 20, 50, 100\}$, $n \in \{10, 15, 20, 25\}$ and two levels of shared variances $R^2 \in \{0.05, 0.1\}$. For each combination of parameters, $k = 1000$ simulations are run. Each test are estimated based on $1000$ randomizations for the $CovLs$ test, or permutations for \texttt{protest} and \texttt{procuste.rtest}.
+To evaluate relative power of the three considered tests, pairs of to random matrices were produced for various $p \in \{10, 20, 50, 100\}$, $n \in \{10, 15, 20, 25\}$ and two levels of shared variations $R^2 \in \{0.05, 0.1\}$. For each combination of parameters, $k = 1000$ simulations are run. Each test are estimated based on $1000$ randomizations for the $CovLs$ test, or permutations for \texttt{protest} and \texttt{procuste.rtest}.
 
 
 
@@ -289,7 +289,7 @@ whatever the $p$ tested (Table~\ref{tab:alpha_pvalue}). This ensure that the pro
                         of the distribution of $P_{values}$ correlation test to $\mathcal{U}(0,1)$
                         under the null hypothesis.\label{tab:alpha_pvalue}} {
 % latex table generated in R 3.5.2 by xtable 1.8-4 package
-% Fri Jun  7 14:46:13 2019
+% Fri Jun  7 15:08:34 2019
 \begin{tabular*}{0.98\linewidth}{@{\extracolsep{\fill}}crrr}
   \hline
   & \multicolumn{3}{c}{Cramer-Von Mises p.value} \\
@@ -306,12 +306,12 @@ whatever the $p$ tested (Table~\ref{tab:alpha_pvalue}). This ensure that the pro
 
 \subsection{Power of the test based on randomisation}
 
-Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is equivalent of the power estimated for both \texttt{vegan::protest} and \texttt{ade4::procuste.rtest} tests (Table \ref{tab:power}). As for the two other tests, power decreases when the number of variable ($p$ or $q$) increases and increase with the number of individuals and the shared variance. The advantage of the test based on the Monte-Carlo estimation of $\overline{RCovLs(X,Y)}$ is to remove the need of running a supplementary set of permutations when \irls is computed.
+Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is equivalent of the power estimated for both \texttt{vegan::protest} and \texttt{ade4::procuste.rtest} tests (Table \ref{tab:power}). As for the two other tests, power decreases when the number of variable ($p$ or $q$) increases and increase with the number of individuals and the shared variation. The advantage of the test based on the Monte-Carlo estimation of $\overline{RCovLs(X,Y)}$ is to remove the need of running a supplementary set of permutations when \irls is computed.
 
 \begin{table}[!t]
-\processtable{Power estimation of the procruste tests for two low level of shared variances $5\%$ and $10\%$.\label{tab:power}} {
+\processtable{Power estimation of the procruste tests for two low level of shared variations $5\%$ and $10\%$.\label{tab:power}} {
 % latex table generated in R 3.5.2 by xtable 1.8-4 package
-% Fri Jun  7 14:46:13 2019
+% Fri Jun  7 15:08:34 2019
 \begin{tabular}{lcrrrrrrrrr}
   \hline
   & $R^2$ & \multicolumn{4}{c}{5\%} & &\multicolumn{4}{c}{10\%} \\
@@ -336,7 +336,8 @@ Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is
 }{} % <- we can add a footnote in the last curly praces
 \end{table}
 
-\subsection{Evaluating the shared variance}
+\subsection{Evaluating the shared variation}
+$\rls$ can be considered for matrices as a strict equivalent of Pearson's $\rpearson$ for vectors. Therefore its squared value is an estimator of the shared variation between two matrices. But because of over-fitting the estimation is over-estimated. The proposed corrected vection ($\irls$) of that coefficient is able to provide a good estimate of the shared variation and is perfectly robust to the over-fitting phenomenon (Figure~\ref{fig:shared_variation}). Only a small over evalution is observable for the low values of simulated shared variation.
 
 \begin{figure*}[!tpb]%figure1
 \begin{knitrout}
@@ -345,7 +346,7 @@ Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is
 
 \end{knitrout}
 \caption{Shared variation ($R^2$) between two matrices is mesured with both the corrected ($\irls$) and the original ($\rls$) versions of the procrustean correlation coefficient. A gradiant of $R^2$ is simulated for two population sizes ($n \in \{10,24\}$) and two numbers of descriptive variables ($p \in \{10,100\}$). The black dashed line corresponds to a perfect match where measured $R^2$ equals the simulated one.}
-\label{fig:shared_variance}
+\label{fig:shared_variation}
 \end{figure*}