12/7/2023 0 Comments Sas calculatorīy the way, both PROC IML and PROC NLMIXED enable you to choose your favorite optimization solver. The confidence interval confirms what we previously saw in the graph of the log-likelihood function: the function is somewhat flat near the optimum, so a 95% confidence interval is wide. The parameter estimate is the same value (0.56) as was found by the NLPNRA routine in SAS/IML. Notice that the output from PROC NLMIXED contains the parameter estimate, standard error, and 95% confidence intervals. Parms p = 0.5 * initial value for parameter * Method 2: Use PROC NLMIXED solve using built-in modeling syntax */ proc nlmixed data=Binomial Some procedure (like the MCMC and NLMIXED) use the p parameter as the second argument: Binom(NTrials, p). Some functions like PDF, CDF, and RAND use the p parameter as the first argument: Binom(p, NTrials). Be sure to ALWAYS check the documentation for the correct syntax for a binomial distribution. On the MODEL statement, you declare that you want to model the X variable as Binom(p) where NTrials=10, and you use the PARMS statement to supply an initial guess for the parameter p. The syntax for PROC NLMIXED is very simple for the Binomial data. (You can also use PROC GENMOD to fit these distributions I have shown an example of fitting Poisson data.) PROC NLMIXED has built-in support for computing maximum likelihood estimates of data that follow theīernoulli (binary), binomial, Poisson, negative binomial, normal, and gamma distributions. In fact, I sometimes joke that SAS could have named the procedure "PROC MLE" because it is so useful for solving maximum likelihood problems. However, you can use the NLMIXED procedure for general maximum likelihood estimation. If you've never used PROC NLMIXED before, you might wonder why I am using that procedure, since this problem is not a mixed modeling regression. Maximum likelihood estimates for binomial data from PROC NLMIXED We conclude that the parameter p=0.56 (with NTrials=10) is "most likely" to be the binomial distribution parameter that generated the data. The NLPNRA subroutine computes that the maximum of the log-likelihood function occurs for p=0.56, which agrees with the graph in the previous article. P0 = 0.5 /* initial guess for solution */ call nlpnra (rc, p_MLE, "Binom_LL", p0, opt, con ) * set constraint matrix, options, and initial guess for optimization */Ĭon = /* print some output */ NTrials = 10 /* number of trials (fixed) */ LL = sum ( logpdf ( "Binomial", x, p, NTrials ) ) Start Binom_LL (p ) global ( x, NTrials ) * log-likelihood function for binomial data */ * Before running program, create Binomial and LN data sets from previous post */ /* Example 1: MLE for binomial data */ /* Method 1: Use SAS/IML optimization routines */ proc iml The following statements define bounds for the parameter (0 < p < 1) and provides an initial guess of p 0=0.5: In my previous article I used the LOGPDF function to define the log-likelihood function for the binomial data. SAS/IML contains many algorithms for nonlinear optimization, including the NLPNRA subroutine, which implements the Newton-Raphson method. I previously wrote a step-by-step description of how to compute maximum likelihood estimates in SAS/IML. Maximum likelihood estimates for binomial data from SAS/IML You canĭownload the SAS program that creates the data and computes these maximum likelihood estimates. One data set contains binomial data, the other contains data that are lognormally distributed. To illustrate these methods, I will use the same data sets from my previous post. This article shows two ways to compute maximum likelihood estimates (MLEs) in SAS: the nonlinear optimization subroutines in SAS/IML and the NLMIXED procedure in SAS/STAT. In a previous article, I showed two ways to define a log-likelihood function in SAS.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |