lmtest (version 0.9-34)

encomptest: Encompassing Test for Comparing Non-Nested Models

Description

encomptest performs the encompassing test of Davidson & MacKinnon for comparing non-nested models.

Usage

encomptest(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 encomptest is called from.

vcov.

a function for estimating the covariance matrix of the regression coefficients, e.g., vcovHC.

...

further arguments passed to waldtest.

Value

An object of class "anova" which contains the residual degrees of freedom in the encompassing model, the difference in degrees of freedom, Wald statistic (either "F" or "Chisq") and corresponding p value.

Details

To compare two non-nested models, the encompassing test fits an encompassing model which contains all regressors from both models such that the two models are nested within the encompassing model. A Wald test for comparing each of the models with the encompassing model is carried out by waldtest. For further details, see the references.

References

R. Davidson & J. MacKinnon (1993). Estimation and Inference in Econometrics. New York, Oxford University Press.

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, jtest

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)

## Encompassing model
fm3 <- lm(con ~ gnp + con1 + 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)

## the encompassing test is essentially
waldtest(fm1, fm3, fm2)