## usethis namespace: start
#' @useDynLib regNselect, .registration = TRUE
## usethis namespace: end
NULL
## usethis namespace: start
#' @importFrom Rcpp sourceCpp
## usethis namespace: end
NULL
#' Linear regression model
#'
#' Performs linear regression using Ordinary Least Squares (or Weighted Least Squares when weights are specified)
#'
#' @param formula Model formula using specified columns of DataFrame 'data'. Can include interactions and select no intercept
#' with -1
#' @param data Dataframe from which model variables are pulled.
#' @param weights Vector of weights to be used in Weighted Least Squares regression estimates. Default = NULL.
#' @return List of coefficients, estimate standard errors, test statistics, and p-values
#'
#' @export
lin_model = function(formula, data, weights= NULL){
if(length(formula[[2]]) != 1){
stop("y must be univariate")
}
modframe = model.frame(formula = formula, data = data)
y <- model.response(modframe, "numeric")
x = model.matrix(formula, data = data)
n = length(y)
if(is.null(weights)){
beta = solve(t(x)%*%x)%*%t(x)%*%y
#beta = betaRcpp(y,x)
res = y - x%*%beta
sigma_sq = sum(res^2)/(n-ncol(x))
varcov_beta = solve(t(x)%*%x)*sigma_sq
} else {
if(!is.vector(weights) | length(weights) != n){
stop("Weights must be written as a vector with length equal to length y")
}
w = diag(weights)
beta = solve(t(x) %*% w %*% x) %*% t(x) %*% w %*% y
#beta = betaRcpp(y,x)
res = y - x%*%beta
sigma_sq <- sum(weights*res^2)/(n - ncol(x))
varcov_beta = sigma_sq* solve(t(x)%*%w%*%x)
}
se_beta =sqrt(diag(varcov_beta))
test_stat = beta/se_beta
p = 2*pt(-abs(test_stat), n-1)
results = cbind.data.frame(coefficients = round(beta,6), St.Error = round(se_beta,6),
test_statistic = round(test_stat,3), p_value = p)
row.names(results) = colnames(x)
return(results)
}
#' Backwards selcection of linear regression model
#'
#' Performs backwards selection of model parameters. Removes parameter with greatest p-value above "prem" threshold.
#' P-values are calculated using Ordinary Least Squares (no weighting option).
#'
#' @param formula Model formula using specified columns of DataFrame 'data'. Can include interactions and select no intercept
#' with -1.
#' @param data Dataframe from which model variables are pulled.
#' @param prem Threshold at which a parameter will be removed from the model if it has the highest p-value above the threshold.
#' The default value is .1.
#' @return Dataframe of coefficients, estimate standard errors, test statistics, and p-values
#' for parameters remaining in the model following backwards selection.
#'
#' @export
back_select = function(formula, data, prem = .1){
if(length(formula[[2]]) != 1){
stop("y must be univariate")
}
modframe = model.frame(formula = formula, data = data)
y <- model.response(modframe, "numeric")
x = model.matrix(formula, data = data)
n = length(y)
beta = solve(t(x)%*%x)%*%t(x)%*%y
#beta = betaRcpp(y,x)
res = y - x%*%beta
q = ifelse(is.matrix(x), ncol(x), 1)
sigma_sq = sum(res^2)/(n-q)
varcov_beta = solve(t(x)%*%x)*sigma_sq
se_beta =sqrt(diag(varcov_beta))
test_stat = beta/se_beta
p = 2*pt(-abs(test_stat), n-1)
removed_vars = c()
while(max(p[2:max(2,q)]) > prem){
rem_col = which(p == max(p[2:ncol(x)]))
removed_vars = c(removed_vars, colnames(x)[rem_col])
x = x[,-rem_col]
beta = solve(t(x) %*% x) %*% t(x) %*% y
res = y - x%*%beta
q = ifelse(is.matrix(x), ncol(x), 1)
sigma_sq = sum(res^2)/(n-q)
varcov_beta = solve(t(x)%*%x)*sigma_sq
se_beta =sqrt(diag(varcov_beta))
test_stat = beta/se_beta
p = 2*pt(-abs(test_stat), n-1)
if(q == 1){break}
}
results = cbind.data.frame(coefficients = round(beta,6), St.Error = round(se_beta,6),
test_statistic = round(test_stat,3), p_value = p)
row.names(results) = c("Intercept",colnames(x)[2:max(2,q)])
cat("Removed variables:\n", removed_vars, "\n")
return(results)
}
#x = rnorm(10)
#x2 = rnorm(10)
#x3 = rnorm(10)
#y = rnorm(10)
#df = data.frame(y, x, x2, x3)
#lin_model(y~x*x2,df)
#back_select(y~x*x2,df,.5)
#summary(lm(y~x*x2, data = df))
#olsrr::ols_regress(y~x*x2, data = df)
#result = bench::mark(lin_model(y~x*x2,df)[1], as.vector(olsrr::ols_regress(y~x*x2, data = df)$beta)[1])
#plot(result)
#result2 = bench::mark(lin_model(y~x*x2,df)[1], as.vector(lm(y~x*x2, data = df)$coefficients[1]))
#plot(result2)
#result3 = bench::mark(lin_model(y~x*x2,df)[1], lin_model2(y~x*x2,df)[1])
#plot(result3)
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