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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: Re: Mysterious Output Given by GLLAMM for Multiple-Equation Generalized Linear Model |

Date |
Sun, 15 Jul 2012 16:30:20 +0900 |

Weihao Yin wrote: I am learning to use GLLAMM to estimate a multiple-equation Generalized Linear Model, which jointly models binary and count data. The dataset I use is about the condition and length of hospital stay for 32 herniorrhaphy patients. The dataset is freely available online. The response variables are [leave] and [los], which denote the condition of the patient upon leaving the operating room and the length of hospital stay after the operation. One of the two covariate is [OKstatus] which distinguishes patients based on their post-operative physical status with "1" indicating better status. The other is patient's age. The model consists of two equations: one is logit model for [leave] and the other is a Poisson model for [los]. The correlation between the two is captured using a common random effect. Mathematically, it is written as: g1([leave]) = b01+b11*[age]+b12*[OKstatus]+u+epsilon1 g2([los]) = b02+b12*[age]+b22*[OKstatus]+u+epsilon2 where u is the random effect and epsilon1&2 are errors. This example is also used in the SAS GLIMMIX procedure documentation (pp. 203-209). I just try to reproduce the results using GLLAMM. Since the random effect is used as an intercept, I use a constraint to make the factor loadings for both equations on the random effect equal to 1. The GLLAMM gives the following output, in which [d1] is the dummy variable for logit and [d2] is Poisson. [output redacted] The output generally is the same as given by the SAS GLIMMIX. However, when I rerun the model using "allc" option to list all the estimated parameters, here is what I got. [output redacted] The last parameter [pat1_1]d1 = 0.5281017. Does anyone know what this parameter is? The first loading "d1" is supposed to be 1 and it is according to the previous output. By the name of it, it seems to be the factor loading. Does GLLAMM estimate the variance of the two epsilons? If it does not, how can I calculate the correlation between the two responses, which is the whole point of this? I know it is a long post but I really need some help. Any input is greatly appreciated. Thanks! -------------------------------------------------------------------------------- I'll try to answer your three questions in turn: 1. [pat1_1]d1 is the variance of the random effect (latent factor) in the form in which it is parameterized during the fitting procedure. For numerical stability reasons and to assure that it is at least positive semidefinite, -gllamm- parameterizes the level-2 variance matrix as a Cholesky decomposition. Because you have only a single variance component, this reduces to a scalar instead of a matrix, and [pat1_1]d1 is therefore the square root of the variance of the random effect. (See the do-file below for illustration.) 2. I believe that -gllamm- doesn't estimate variances for any epsilons inside the linear predictor equation for one-parameter distributions, such as binomial and Poisson. It won't estimate separate variances of level-1 epsilons in linear models, either, unless you use the -s()- option. 3. You don't really compute the intraclass correlation coefficient when you have a Poisson response variable. You can point to the nonzero variance of the random effect as evidence that the binary and count response variables are substantially correlated. As an aside, based upon what I infer your command line must have been (see first -gllamm- syntax in the do-file below), you could have specified the same model a bit more simply. With this model, you can omit the factor-loading equation and the subsequently necessitated constraint on the second loading. (See the second syntax in the do-file below.) Joseph Coveney drop _all input byte patient byte age str1 gender /// byte OKstatus byte leave byte los [dataset omitted for brevity--see http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm #statug_glimmix_sect017.htm for its listing] end rename leave response1 rename los response2 quietly reshape long response, i(patient) j(dist) quietly tabulate dist, generate(d) generate byte d1Xage = d1 * age generate byte d2Xage = d2 * age generate byte d1XOKstatus = d1 * OKstatus generate byte d2XOKstatus = d2 * OKstatus * * What I assume your model is * eq manifest: d1 d2 constraint define 1 [pat1_1l]d2 = 1 gllamm response d1 d2 d1Xage d2Xage /// d1XOKstatus d2XOKstatus, /// noconstant i(patient) /// eqs(manifest) constraints(1) /// family(binomial poisson) fv(dist) /// link(logit log) lv(dist) /// <- optional adapt allc nolog // What [pat1_1]d1 is . . . display in smcl as text _b[pat1_1:d1]^2 // cf. "level2 (patient) var(1): .27889147" * * Same model, slightly simpler syntax * gllamm response d1 d2 d1Xage d2Xage /// d1XOKstatus d2XOKstatus, /// noconstant i(patient) /// family(binomial poisson) fv(dist) /// link(logit log) lv(dist) /// <- optional adapt allc nolog exit * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Mysterious Output Given by GLLAMM for Multiple-Equation Generalized Linear Model***From:*"Weihao Yin" <alexyin@vt.edu>

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