Likelihood in Lander and Botstein 1989

Dahlia Nielsen dahlia at
Tue Apr 9 15:21:07 EST 1996

On 3 Apr 1996
Dr. Gerard Tromp said:

>         I've been trying to grasp the Lander and Botstein article "Mapping
> Mendelian Factors Underlying Quantitative Traits Using RFLP Linkage Maps"
> Genetics 121:185-199.
> The QUESTION I have is about the unlinked likelihood for the likelihood ratio
> test.
>         L&B state: "These constrained MLEs are easily seen to be
>                     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> (mean of A, 0, var(B1))."
> ^^^^^^^^^^^^^^^^^^^^^^^^
> where A is the low phenotype strain and B1 is the
> F1 X A backcross. What I don't understand is the estimate of the "mean of
> A", the other two are easily seen. I expected the estimate of the mean to
> revert to that of the population under study, i.e. B1. 

Carbonell, et. al. (Biometrics 48:305-315) note on page 312 "It
appears [this] is a printing error in the paragraph below their
formula (4) and the formula immediately after (Lander, personal
communication), because in the constrained model the best estimate for
<mean> should be the sample phenotypic mean, <mu hat>."  (<mu hat> is
the MLE of <mean>, which should be the est of mean of B1, as you

Hope this helps.

Dahlia Nielsen
Program in Statistical Genetics
North Carolina State University

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