RESET Test for Fractional Response Regressions under Neglected Heterogeneity

fracreghet.reset is used to test the specification of fractional response models estimated by GMMx or LINx.

Usage

fracreghet.reset(object, lastpower.vec = 3, version = "Wald", table = T, ...)

Arguments

object: an object containing the results of an fracreghet command.
lastpower.vec: a numeric vector containing the maximum powers of the linear predictors to be used in RESET tests.
version: a vector containing the test versions to use. Available options: Wald (the default) and LM (only available for GMMx).
table: a logical value indicating whether a summary table with the test results should be printed.
...: Arguments to pass to nlminb, which is used to estimate the model under the alternative hypothesis when version is equal to "Wald" and the null model was estimated by GMMx.

Details

fracreghet.reset applies the RESET test statistic to fractional response models estimated via fracreghet using the options GMMx or LINx. fracreghet.reset may be used to test simultaneously the validity of the link specification and the transformation applied to the response variable by each estimator.

RESET Test under Unobserved Heterogeneity: The test is based on augmenting the original model with powers of the linear predictor $x\hat{\beta}$. For GMMx, it tests $H_0: \gamma = 0$ in the expanded moment conditions: $$E\left[Z_i \left(H(y_i) - \exp\left(x_i\beta + \sum_{k=2}^P \gamma_k (x_i\hat{\beta})^k\right)E(e^{c_i})\right)\right] = 0$$ This simultaneously evaluates whether the mean function and the specific heterogeneity transformation $H(\cdot)$ are correctly specified.

It is taken into account the option that was chosen for computing standard errors in the model under evaluation. See Ramalho and Ramalho (2017) for details.

Value

fracreghet.reset returns a named vector with the test results.

References

Ramalho, E. A., & Ramalho, J. J. S. (2017), "Moment-based estimation of nonlinear regression models with boundary outcomes and endogeneity, with applications to nonnegative and fractional responses", Econometric Reviews, 36(4), 397-420.

Ramsey, J.B. (1969), "Tests for Specification Errors in Classical Linear Least-Squares Regression Analysis", Journal of the Royal Statistical Society: Series B (Methodological), 31(2), 350-371.

Author

Sulman Olieko Owili <oliekosulman@gmail.com>

Examples

### Empirical 401(k) Examples 
data("fracreg_k401k") 
y <- fracreg_k401k$prate 
X_het <- cbind(mrate = fracreg_k401k$mrate, ltotemp = fracreg_k401k$ltotemp)
 
# fracreghet estimators do not allow exact 1s or 0s
y_adj <- y
y_adj[y_adj == 1] <- 0.999

# Instrument mrate using age

Z_emp <- cbind(age = fracreg_k401k$age, ltotemp = fracreg_k401k$ltotemp) 
res_emp <- fracreghet(y_adj, X_het, type="GMMx", link="logit", table=FALSE) 
fracreghet.reset(res_emp)
#> 
#> -------------------------------------------------------------------------------- 
#>                                    RESET test 
#> -------------------------------------------------------------------------------- 
#>                           Fractional logit regression 
#> -------------------------------------------------------------------------------- 
#> H0: Estimator: GMMx 
#> -------------------------------------------------------------------------------- 
#>         Statistic p-value    
#> Wald(3)     47.56 4.7e-11 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> -------------------------------------------------------------------------------- 
#>                          Run Date: 2026-07-06 15:19:38 
#> -------------------------------------------------------------------------------- 
 
### Simulated Examples

N <- 250
u <- rnorm(N)

X <- cbind(rnorm(N),rnorm(N))
dimnames(X)[[2]] <- c("X1","X2")

Z <- cbind(rnorm(N),rnorm(N),rnorm(N))
dimnames(Z)[[2]] <- c("Z1","Z2","Z3")

y <- exp(X[,1]+X[,2]+u)/(1+exp(X[,1]+X[,2]+u))

res <- fracreghet(y,X,type="GMMx",table=FALSE)

#LM and Wald versions of the RESET test, based on 1 or 2 fitted powers of xb
fracreghet.reset(res,2:3,c("Wald","LM"))
#> 
#> -------------------------------------------------------------------------------- 
#>                                    RESET test 
#> -------------------------------------------------------------------------------- 
#>                           Fractional logit regression 
#> -------------------------------------------------------------------------------- 
#> H0: Estimator: GMMx 
#> -------------------------------------------------------------------------------- 
#>         Statistic p-value  
#> LM(2)       0.216  0.6424  
#> Wald(2)     0.180  0.6711  
#> LM(3)       3.481  0.1754  
#> Wald(3)     6.273  0.0434 *
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> -------------------------------------------------------------------------------- 
#>                          Run Date: 2026-07-06 15:19:38 
#> --------------------------------------------------------------------------------