inst/shiny-squid/source/pages/full_model_sbys/ui_fullmodel_sbys_full_model.R

In squid: Statistical Quantification of Individual Differences

myTable <-  data.frame(
              "Components"   = c(paste("$",NOT$time,"$",sep=""), 
                                 paste("$",NOT$ind,"$",sep=""),  
                                 paste("$",NOT$group,"$",sep=""), 
                                 paste("$",EQ$phen.1,"$", sep=""),
                                 paste("$",EQ$phen.2,"$", sep=""),
                                 paste("$",NOT$mean,"_0$",sep=""), 
                                 paste("$",NOT$devI,"_",NOT$ind,"$",sep=""), 
                                 paste("$",NOT$mean," ",NOT$env,"$",sep=""),
                                 paste("$",NOT$devS,"_",NOT$ind,NOT$env,"$",sep=""),
                                 paste("$",NOT$groupV,"_",NOT$group,"$",sep=""),
                                 paste("$",NOT$error,"_{",NOT$time,NOT$ind,NOT$group,"}$",sep="")
                                ),
              "Explanations" = c("Instance of time.",
                                "Individual identifier.",
                                "Group identifier.",
                                paste("Phenotypic value of trait $",NOT$trait.1,"$ at instance $",NOT$time,"$ for individual $",NOT$ind,"$ within group $",NOT$group,"$.",sep=""),
                                paste("Phenotypic value of trait $",NOT$trait.2,"$ at instance $",NOT$time,"$ for individual $",NOT$ind,"$ within group $",NOT$group,"$.",sep=""),
                                "Population mean",
                                paste("Individual-specific deviations (random-intercepts) for individual $",NOT$ind,"$.",sep=""),
                                paste("Population mean response to environmental influences $",NOT$env,"$.",sep=""),
                                paste("Individual-specific response to environmental influences $",NOT$env,"$ (random-slope) for individual $",NOT$ind,"$.",sep=""),
                                paste("Higher-level grouping for each group $",NOT$group,"$.",sep=""),
                                paste("Residual for the individual $",NOT$ind,"$ and the group $",NOT$group,"$ at time $",NOT$time,"$.",sep="")
              )
)

myDefinitionTable    <- getTable(myTable)

myVarCovMatrix       <- paste(
"$$ \\begin{pmatrix}",
        EQ$dev0.1 , "\\\\",
        EQ$dev1.1 , "\\\\",
        EQ$dev2.1 , "\\\\",
        EQ$dev12.1, "\\\\",
        EQ$dev0.2 , "\\\\",
        EQ$dev1.2 , "\\\\",
        EQ$dev2.2 , "\\\\",
        EQ$dev12.2, "\\\\
    \\end{pmatrix}
        \\sim MNV(0,\\Omega_{",NOT$devI, NOT$devS,"}):
        \\Omega_{",NOT$devI, NOT$devS,"}=
    \\begin{pmatrix}
        Var(",   EQ2$dev0.1,")                  &                                      &                                    &                                     &                                    &                                    &                                    &                    \\\\
        Cov(", EQ2$dev0.1, ",", EQ2$dev1.1 ,") & Var(",   EQ2$dev1.1, ")                &                                    &                                     &                                    &                                    &                                    &                    \\\\
        Cov(", EQ2$dev0.1, ",", EQ2$dev2.1 ,") & Cov(", EQ2$dev1.1, ",",EQ2$dev2.1 ,") & Var(",  EQ2$dev2.1,")                &                                     &                                    &                                    &                                    &                    \\\\
        Cov(", EQ2$dev0.1, ",", EQ2$dev12.1,") & Cov(", EQ2$dev1.1, ",",EQ2$dev12.1,") & Cov(",EQ2$dev2.1,",",EQ2$dev12.1,") & Var(",  EQ2$dev12.1,")                &                                    &                                    &                                    &                    \\\\
        Cov(", EQ2$dev0.1, ",", EQ2$dev0.2 ,") & Cov(", EQ2$dev1.1, ",",EQ2$dev0.2 ,") & Cov(",EQ2$dev2.1,",",EQ2$dev0.2 ,") & Cov(",EQ2$dev12.1,",",EQ2$dev0.2 ,") & Var(",  EQ2$dev0.2,")                &                                    &                                    &                    \\\\
        Cov(", EQ2$dev0.1, ",", EQ2$dev1.2 ,") & Cov(", EQ2$dev1.1, ",",EQ2$dev1.2 ,") & Cov(",EQ2$dev2.1,",",EQ2$dev1.2 ,") & Cov(",EQ2$dev12.1,",",EQ2$dev1.2 ,") & Cov(",EQ2$dev0.2,",",EQ2$dev1.2 ,") & Var(",EQ2$dev1.2,")                  &                                    &                    \\\\
        Cov(", EQ2$dev0.1, ",", EQ2$dev2.2 ,") & Cov(", EQ2$dev1.1, ",",EQ2$dev2.2 ,") & Cov(",EQ2$dev2.1,",",EQ2$dev2.2 ,") & Cov(",EQ2$dev12.1,",",EQ2$dev2.2 ,") & Cov(",EQ2$dev0.2,",",EQ2$dev2.2 ,") & Cov(",EQ2$dev1.2,",",EQ2$dev2.2 ,") & Var(",EQ2$dev2.2,")                  &                    \\\\
        Cov(", EQ2$dev0.1, ",", EQ2$dev12.2,") & Cov(", EQ2$dev1.1, ",",EQ2$dev12.2,") & Cov(",EQ2$dev2.1,",",EQ2$dev12.2,") & Cov(",EQ2$dev12.1,",",EQ2$dev12.2,") & Cov(",EQ2$dev0.2,",",EQ2$dev12.2,") & Cov(",EQ2$dev1.2,",",EQ2$dev12.2,") & Cov(",EQ2$dev2.2,",",EQ2$dev12.2,") & Var(",EQ2$dev12.2,") \\\\
    \\end{pmatrix} 
$$",sep="")

myG      <- paste("$$",NOT$groupV,"_{",NOT$group,"} \\sim N(0,Var(",NOT$groupV,"))$$", sep="")
mye      <- paste("$$",NOT$error,"_{",NOT$time,NOT$ind,NOT$group,"} \\sim N(0,Var(",NOT$error,"))$$", sep="")

span( 
	p(HTML(fullmodelTxt$SimModel_intro)), 
		 
	h4("Model equation"),

	source("./source/pages/full_model_sbys/ui_fullmodel_equation.R",local=TRUE)[["value"]],

	myDefinitionTable,

	p(HTML(fullmodelTxt$modelEquation_1)),
	p(HTML(fullmodelTxt$modelEquation_2)),
	p(HTML(fullmodelTxt$modelEquation_3)),
	p(HTML(fullmodelTxt$modelEquation_4)),
	p(HTML(fullmodelTxt$modelEquation_5)),
	p(HTML(fullmodelTxt$modelEquation_6)),
	p(HTML(fullmodelTxt$modelEquation_7)),

	h4("Individual specific responses"),
	p(HTML(fullmodelTxt$indSpecResponses)),
	myVarCovMatrix,
	p(HTML("Some of the terms above are explained in more detail in the two following sections (i.e., <i>Model summary</i> and <i>Bivariate model</i>)")),

	h4("Environments"),
	p(HTML(fullmodelTxt$environment_1)),
	p(HTML(fullmodelTxt$environment_2)),
	p(HTML(fullmodelTxt$environment_3)),
	p(HTML(fullmodelTxt$environment_4)),
	p(HTML(fullmodelTxt$environment_5)),
	p(HTML(fullmodelTxt$environment_6)),
	p(HTML('<figure>
		  <img src="pictures/Environment_examples.jpg" alt="Environmental effects.">
		  <figcaption><b>Figure 1:</b> example of 3 environmental effects. 
								  (Left) Linear trend with some stochasticity 
								  (Middle) Cyclic pattern with linear trend and some stochasticity. 
								  (Right) Autocorrelation of 0.7 added to stochastic values.</figcaption>
		  </figure>')
	),
	p(HTML(fullmodelTxt$environment_7)),
	p(HTML('<figure>
		  <img src="pictures/shared_vs_unshared_examples.jpg" alt="Shared and unshared environmental effects">
		  <figcaption><b>Figure 2:</b> example of 2 environments, one shared (left) and one unshared (right) between 3 individuals. 
																	 Both environments have been generated with stochastic, linear, and cyclic effect.</figcaption>
		  </figure>')
	),
	p(HTML(fullmodelTxt$environment_8)),

	h4("High-level grouping and residual"),
	p(HTML(fullmodelTxt$groupingNerror)),
	myG,
	mye
)