Chow's test for heterogeneity in two regressions

Description

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.

Usage

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

Arguments

Details

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

Source

http://aoki2.si.gunma-u.ac.jp/R/

References

Chow GC (1960). Tests of equality between sets of coefficients in two linear regression. Econometrica 28:591-605

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)

## End(Not run)