chow.test {gap}

Chow's test for heterogeneity in two regressions

Description

Chow's test for heterogeneity in two regressions

Usage

chow.test(y1, x1, y2, x2, x = NULL)

Arguments

y1

a vector of dependent variable.

x1

a matrix of independent variables.

y2

a vector of dependent variable.

x2

a matrix of independent variables.

x

a known matrix of independent variables.

Details

Chow's test is for differences between two or more regressions. Assuming that errors in regressions 1 and 2 are normally distributed with zero mean and homoscedastic variance, and they are independent of each other, the test of regressions from sample sizes n_1 and n_2 is then carried out using the following steps. 1. Run a regression on the combined sample with size n=n_1+n_2 and obtain within group sum of squares called S_1. The number of degrees of freedom is n_1+n_2-k, with k being the number of parameters estimated, including the intercept. 2. Run two regressions on the two individual samples with sizes n_1 and n_2, and obtain their within group sums of square S_2+S_3, with n_1+n_2-2k degrees of freedom. 3. Conduct an F_{(k,n_1+n_2-2k)} test defined by

F = \frac{[S_1-(S_2+S_3)]/k}{[(S_2+S_3)/(n_1+n_2-2k)]}

If the F statistic exceeds the critical F, we reject the null hypothesis that the two regressions are equal.

In the case of haplotype trend regression, haplotype frequencies from combined data are known, so can be directly used.

Value

The returned value is a vector containing (please use subscript to access them):

• F the F statistic.

• df1 the numerator degree(s) of freedom.

• df2 the denominator degree(s) of freedom.

• p the p value for the F test.

Note

adapted from chow.R.

Author(s)

Shigenobu Aoki, Jing Hua Zhao

References

Chow GC (1960). “Tests of Equality Between Sets of Coefficients in Two Linear Regressions.” Econometrica, 28(3), 591-605. ISSN 00129682, 14680262, doi:10.2307/1910133.

See Also

htr

Examples

## Not run: 
dat1 <- matrix(c(
     1.2, 1.9, 0.9,
     1.6, 2.7, 1.3,
     3.5, 3.7, 2.0,
     4.0, 3.1, 1.8,
     5.6, 3.5, 2.2,
     5.7, 7.5, 3.5,
     6.7, 1.2, 1.9,
     7.5, 3.7, 2.7,
     8.5, 0.6, 2.1,
     9.7, 5.1, 3.6), byrow=TRUE, ncol=3)

dat2 <- matrix(c(
     1.4, 1.3, 0.5,
     1.5, 2.3, 1.3,
     3.1, 3.2, 2.5,
     4.4, 3.6, 1.1,
     5.1, 3.1, 2.8,
     5.2, 7.3, 3.3,
     6.5, 1.5, 1.3,
     7.8, 3.2, 2.2,
     8.1, 0.1, 2.8,
     9.5, 5.6, 3.9), byrow=TRUE, ncol=3)

y1<-dat1[,3]
y2<-dat2[,3]
x1<-dat1[,1:2]
x2<-dat2[,1:2]
chow.test.r<-chow.test(y1,x1,y2,x2)
# from http://aoki2.si.gunma-u.ac.jp/R/

## End(Not run)