R: J Test for Comparing Non-Nested Models

jtest {lmtest} | R Documentation

## J Test for Comparing Non-Nested Models

### Description

`jtest` performs the Davidson-MacKinnon J test for comparing non-nested models.

### Usage

     jtest(formula1, formula2, data = list(), vcov. = NULL, ...)

### Arguments

`formula1` | either a symbolic description for the first model to be tested, or a fitted object of class `"lm"`.
`formula2` | either a symbolic description for the second model to be tested, or a fitted object of class `"lm"`.
`data` | an optional data frame containing the variables in the model. By default the variables are taken from the environment which `jtest` is called from.
`vcov.` | a function for estimating the covariance matrix of the regression coefficients, e.g., `vcovHC`.
`...` | further arguments passed to `coeftest`.

### Details

The idea of the J test is the following: if the first model contains the correct set of regressors, then including the fitted values of the second model into the set of regressors should provide no significant improvement. But if it does, it can be concluded that model 1 does not contain the correct set of regressors.

Hence, to compare both models the fitted values of model 1 are included into model 2 and vice versa. The J test statistic is simply the marginal test of the fitted values in the augmented model. This is performed by `coeftest`.

For further details, see the references.

### Value

An object of class `"anova"` which contains the coefficient estimate of the fitted values in the augmented regression plus corresponding standard error, test statistic and p value.

### References

R. Davidson & J. MacKinnon (1981). Several Tests for Model Specification in the Presence of Alternative Hypotheses. Econometrica, 49, 781-793.

W. H. Greene (1993), Econometric Analysis, 2nd ed. Macmillan Publishing Company, New York.

W. H. Greene (2003). Econometric Analysis, 5th ed. New Jersey, Prentice Hall.

### See Also

`coxtest`, `encomptest`

### Examples

    ## Fit two competing, non-nested models for aggregate
    ## consumption, as in Greene (1993), Examples 7.11 and 7.12

    ## load data and compute lags
    data(USDistLag)
    usdl <- na.contiguous(cbind(USDistLag, lag(USDistLag, k = -1)))
    colnames(usdl) <- c("con", "gnp", "con1", "gnp1")

    ## C(t) = a0 + a1*Y(t) + a2*C(t-1) + u
    fm1 <- lm(con ~ gnp + con1, data = usdl)

    ## C(t) = b0 + b1*Y(t) + b2*Y(t-1) + v
    fm2 <- lm(con ~ gnp + gnp1, data = usdl)

    ## Cox test in both directions:
    coxtest(fm1, fm2)

    ## ...and do the same for jtest() and encomptest().
    ## Notice that in this particular case they are coincident.
    jtest(fm1, fm2)
    encomptest(fm1, fm2)

[Package lmtest version 0.9-37 Index]