Under the null hypothesis the probability for a parent to transmit either allele to an affected subject is 0.5:
Pij = Pji = 0.5
For each allele we can define a parameter, Bx, which gives a measure of how likely that allele is to be transmitted from a heterozygous parent to an affected subject. Then we can define the relative probabilities for a parent who has genotype IJ to transmit allele I or allele J as follows:
ln(Pij/Pji) = Bi - Bj (or Pij/Pji = eBi-Bj)
We can then maximise the likelihood of the observed data by letting the B's take different values (except for one of them which we arbitrarily set to zero). This process is called logistic regression.
If we write the likelihood for the data maximised over these allele parameters as L1 and that under the the null hypothesis (with all Pij=0.5) as L0, then we can obtain a likelihood ratio statistic which is 2ln(L1/L0). This is a chi-squared statistic with degrees of freedom one less than the number of alleles.