13.1 Introduction to lm_map

The program lm_map finds the maximum likelihood estimate (MLE) of the marker map, estimates the variance of the MLE, and tests hypotheses about the true map. All inference is based on the analysis of multilocus marker data obtained from some (possibly all) members of a set of independent families.

To find the MLE, lm_map uses either Monte Carlo expectation- maximization (MCEM) or a hybrid of MCEM and stochastic approximation (SA). In either case, the user must supply an initial map estimate, and an initial Monte Carlo (MC) sample size for the MCEM algorithm. The MCEM sample size is automatically increased with each successive step of the algorithm, and only a small number of MCEM steps are needed to estimate the MLE. If the hybrid option is chosen, lm_map uses the MCEM estimate to seed the SA algorithm. Then, a relatively large number of SA steps are used to estimate the MLE with greater precision.

Once the MLE is obtained, a long Markov chain is used to estimate the variance of the MLE. Finally, a slight adaptation of the MC likelihood ratio formula is used to estimate the likelihood ratio test (LRT) statistics for testing the simple and/or composite null hypotheses. For more details, see Stewart, WCL and Thompson, EA (2006) Improving estimates of genetic maps: A maximum likelihood approach. Biometrics 62, 728-734.