```
#' Hausman Specification Test for Two List Experiment Regression Fit Objects
#'
#' @param ml Maximum likelihood model fit, for example from ictreg(method = "nls")
#' @param nls NLS model fit, for example from ictreg(method = "nls")
#' @param abs Flag to override error when Hausman statistic is negative, which may indicate misspecification. Set to \code{FALSE} to override.
#' @param psd Flag to override error when variance-covariance difference is non-positive semidefinite, suggesting misspecification. Set to \code{TRUE} to override.
#'
#' @return List containing Hausman statistic, p-value, and the degrees of freedom of the test.
ict.hausman.test <- function(ml, nls, abs = FALSE, psd = FALSE){
if(length(coef(ml)) != length(coef(nls))){
stop("Please provide two ictreg fit objects that used the same number of covariates.")
}
psd.check <- min(eigen(vcov(nls) - vcov(ml))$values) < 0
stat <-
as.numeric((coef(ml) - coef(nls)) %*%
ginv((vcov(nls) - vcov(ml))) %*%
(coef(ml) - coef(nls)))
# we found that the following check for positive semi-definiteness led to
# significant overrejection of the null
if (psd.check & psd) stop("The variance-covariance difference is non-positive semidefinite, suggesting misspecification. Set psd = FALSE to compute anyway.")
if (stat < 0 & !abs) stop("Hausman test statistic is negative, suggesting possible misspecification. Set abs = TRUE to compute anyway.")
df <- length(coef(ml))
p <- pchisq(q = abs(stat), df = df, lower.tail = FALSE)
return(structure(list(stat = stat, df = df, p = p), class = "ict.hausman.test"))
}
print.ict.hausman.test <- function(x, ...){
cat("\nTest for List Experiment Model Misspecification\n\n")
cat("Hausman statistic = ", x$stat, ", df = ", x$df, ", p-value = ", x$p, ".", sep = "")
cat("\n")
}
```

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