cmtest {cmtest}

Conditional moments test

Description

Conditional moments tests for maximum likelihood estimators consist on adding to the matrix of individual contributions to the score moments conditions and then test the hypothesis that the expected value of the vector of augmented scores is zero. It is particularly convenient for the probit and the tobit model to test for functional form, omitted variables, heteroscedasticity and normaliy.

Usage

cmtest(
  x,
  test = c("normality", "reset", "heterosc", "skewness", "kurtosis"),
  powers = 2:3,
  heter_cov = NULL,
  OPG = FALSE
)

## S3 method for class 'tobit'
cmtest(
  x,
  test = c("normality", "reset", "heterosc", "skewness", "kurtosis"),
  powers = 2:3,
  heter_cov = NULL,
  OPG = FALSE
)

## S3 method for class 'tobit1'
cmtest(
  x,
  test = c("normality", "reset", "heterosc", "skewness", "kurtosis"),
  powers = 2:3,
  heter_cov = NULL,
  OPG = FALSE
)

## S3 method for class 'censReg'
cmtest(
  x,
  test = c("normality", "reset", "heterosc", "skewness", "kurtosis"),
  powers = 2:3,
  heter_cov = NULL,
  OPG = FALSE
)

## S3 method for class 'glm'
cmtest(
  x,
  test = c("normality", "reset", "heterosc", "skewness", "kurtosis"),
  powers = 2:3,
  heter_cov = NULL,
  OPG = FALSE
)

Arguments

x

a fitted model, currently a tobit model either fitted by AER::tobit or censReg::censReg or a probit model fitted by glm with family = binomial(link = 'probit'),

test

the kind of test to be performed, either a normality test (or separately a test that the skewness or kurtosis coefficients are 0 and 3), a heteroscedasticity test or a reset test,

powers

the powers of the fitted values that should be used in the reset test,

heter_cov

a one side formula that indicates the covariates that should be used for the heteroscedasticity test (by default all the covariates used in the regression are used),

OPG

a boolean, if FALSE (the default), the analytic derivatives are used, otherwise the outer product of the gradient formula is used

Value

a list with class 'htest' containing the following components:

• data.mane: a character string describing the fitted model

• statistic: the value of the test statistic

• parameter: degrees of freedom

• p.value: the p.value of the test

• method: a character indicating what type of test is performed

Author(s)

Yves Croissant

References

Newey WK (1985). “Maximum Likelihood Specification Testing and Conditional Moment Tests.” Econometrica, 53(5), 1047–1070. ISSN 00129682, 14680262, https://www.jstor.org/stable/1911011.

Pagan A, Vella F (1989). “Diagnostic Tests for Models Based on Individual Data: A Survey.” Journal of Applied Econometrics, 4, S29–S59. ISSN 08837252, 10991255, https://www.jstor.org/stable/2096593.

Tauchen G (1985). “Diagnostic testing and evaluation of maximum likelihood models.” Journal of Econometrics, 30(1), 415-443. ISSN 0304-4076, doi: 10.1016/0304-4076(85)90149-6, https://www.sciencedirect.com/science/article/pii/0304407685901496.

Wells C (2003). “Retesting Fair's (1978) Model on Infidelity.” Journal of Applied Econometrics, 18(2), 237–239. ISSN 08837252, 10991255, https://www.jstor.org/stable/30035205.

Examples

# replication of Wells (2003) and Pagan and Vella (1989) using Fair's data
library("AER")
data("Affairs", package = "AER")
z <- tobit(affairs ~ gender + age + yearsmarried + children + religiousness +
                     education + occupation + rating, data = Affairs)
cmtest(z, test = "normality")
cmtest(z, test = "skewness", OPG = TRUE)
cmtest(z, test = "kurtosis", OPG = TRUE)
cmtest(z, test = "reset", powers = 2, OPG = TRUE)
cmtest(z, test = "reset", powers = 3, OPG = TRUE)
cmtest(z, test = "heterosc", OPG = TRUE, heter_cov = ~ gender)