Update README

README.Rmd

@@ -32,20 +32,22 @@ Please install the developmental version of the [`{iprior}`](https://github.com/
 
 ## Simulation study
 
-Data pairs $(y_i,x_i)$, where \$x_i\\in\\mathbb R^3\$ for \$i=1,\\dots,n\$, were simulated according to the following model
+Data pairs $(y_i,x_i)$, where $x_i\in\mathbb R^3$ for $i=1,\dots,n$, were simulated according to the following model
 
-\$$
-y_i = \\beta_1 x_{i1} + \\beta_2 x_{i2} + \\beta_3 x_{i3} + \\beta_4 x_{i1}x_{i2} + \\beta_5 x_{i1}x_{i3} + \\beta_6 x_{i2}x_{i3} + \\beta_7 x_{i1}x_{i2}x_{i3} + \\epsilon_i
-\$$
+$$
+y_i = \beta_1 x_{i1} + \beta_2 x_{i2} + \beta_3 x_{i3} + \beta_4 x_{i1}x_{i2} + \beta_5 x_{i1}x_{i3} + \beta_6 x_{i2}x_{i3} + \beta_7 x_{i1}x_{i2}x_{i3} + \epsilon_i
+$$
 
-where \$\\epsilon_i\\sim N(0,\\sigma^2)\$ such that \$\\text{Corr}(\\epsilon_i,\\epsilon_j)=\\rho\$, for \$i\\neq j\$. The simulation settings were \$n=100\$, \$\\sigma=3\$, \$\\rho\\in\\{0,0.5\\}\$. The coefficients were varied according to the table below
+where $\epsilon_i\sim N(0,\sigma^2)$ such that $\operatorname{Corr}(x_{ij},x_{ik})=\rho$, for $j\neq k$. 
+The simulation settings were $n=100$, $\sigma=3$, and $\rho\in\{0,0.5\}$. 
+The coefficients were varied according to the table below
 
 ```{r}
 <<read_model_code>>
 kbl(beta_vals, format = "pipe", row.names = TRUE)
 ```
 
-For each set of true values of the coefficients, the four methods proposed the likeliest model to have generated the data set, from a search of hierarchically nested interaction models. This was replicated a total of \$B=10,000\$ times for each true value set.
+For each set of true values of the coefficients, the four methods proposed the likeliest model to have generated the data set, from a search of hierarchically nested interaction models. This was replicated a total of $B=10,000$ times for each true value set.
 
 The results below show proportion of times that each method selected the true model (higher is better).
 
@@ -125,7 +127,3 @@ mutate(res3, formula = paste0("`", formula, "`")) %>%
 ```{r}
 sessioninfo::session_info()
 ```
-
-
-
-

README.md

@@ -25,17 +25,17 @@ Please install the developmental version of the
 
 ## Simulation study
 
-Data pairs $(y_i,x_i)$, where \$x_i\in\mathbb R^3\$ for \$i=1,\dots,n\$,
+Data pairs $(y_i,x_i)$, where $x_i\in\mathbb R^3$ for $i=1,\dots,n$,
 were simulated according to the following model
 
-\$\$ y_i = \beta_1 x\_{i1} + \beta_2 x\_{i2} + \beta_3 x\_{i3} + \beta_4
-x\_{i1}x\_{i2} + \beta_5 x\_{i1}x\_{i3} + \beta_6 x\_{i2}x\_{i3} +
-\beta_7 x\_{i1}x\_{i2}x\_{i3} + \epsilon_i \$\$
+$$
+y_i = \beta_1 x_{i1} + \beta_2 x_{i2} + \beta_3 x_{i3} + \beta_4 x_{i1}x_{i2} + \beta_5 x_{i1}x_{i3} + \beta_6 x_{i2}x_{i3} + \beta_7 x_{i1}x_{i2}x_{i3} + \epsilon_i
+$$
 
-where \$\epsilon_i\sim N(0,\sigma^2)\$ such that
-\$\text{Corr}(\epsilon_i,\epsilon_j)=\rho\$, for \$i\neq j\$. The
-simulation settings were \$n=100\$, \$\sigma=3\$, \$\rho\in\\0,0.5\\\$.
-The coefficients were varied according to the table below
+where $\epsilon_i\sim N(0,\sigma^2)$ such that
+$\operatorname{Corr}(x_{ij},x_{ik})=\rho$, for $j\neq k$. The simulation
+settings were $n=100$, $\sigma=3$, and $\rho\in\{0,0.5\}$. The
+coefficients were varied according to the table below
 
 |     |  x1 |  x2 |  x3 | x1x2 | x1x3 | x2x3 | x1x2x3 | code    |
 |:----|----:|----:|----:|-----:|-----:|-----:|-------:|:--------|
@@ -51,7 +51,7 @@ The coefficients were varied according to the table below
 For each set of true values of the coefficients, the four methods
 proposed the likeliest model to have generated the data set, from a
 search of hierarchically nested interaction models. This was replicated
-a total of \$B=10,000\$ times for each true value set.
+a total of $B=10,000$ times for each true value set.
 
 The results below show proportion of times that each method selected the
 true model (higher is better).