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Bob H posted on Wednesday, June 09, 2004 - 5:14 pm
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Is it possible to model rates in Mplus when each observation has a numerator and denominator (e.g., either a binomial rate or a Poisson rate)? For example, if observations are at the hospital-level, hospital k would have d(k) deaths arising from n(k) surgeries. For Poisson (count) data it is usual to specify log(n(k)) as an independent variable with its coefficient fixed at 1 (offset term). |
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We don't explicitly model rates in Mplus, but we do allow the regression of one count variable on another count variable. Can you send the reference for your last sentence? |
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Bob H posted on Thursday, June 10, 2004 - 4:11 pm
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I don't have a reference handy, but the idea is straightforward. A Poisson regression is usually written as a (generalized) log-linear model. For example if Y is a Poisson count: log(Y) = a + bx If you want to model the rate, say the count per month, and you observe a count of Y in M months, then you could model the count per month: log(Y/M) = a + bx which can be rewritten: log(Y) = a + bx + log(M) The term log(M) is called an offset because its coefficient is forced to have a value of 1.0 (it is not estimated). Can this model be fit in Mplus? Is there a way to constrain a regression coefficient to have a constant value in Mplus? |
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bmuthen posted on Thursday, June 10, 2004 - 4:20 pm
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This looks doable in Mplus V3. You would declare Y as a count variable (either Poisson or zero-inflated Poisson) in the Variable command and then in the model command you specify the regression y on x logM@1; so that you estimate the intercept and the slope for x, while the slope for the new variable logM (created in the Define command) has its slope fixed at 1. |
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Bob H posted on Thursday, June 10, 2004 - 10:18 pm
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Terrific! Thanks. So we can model Poisson rates. I think we can also model binomial rates. For the binomial each observation has k(i) out of n(i) trials. I want to use logistic regression to model the success rate p(i), which might depend on some covariates x(i), so we are assuming k(i) is distributed as binomial[n(i),p(i)]. I can replace each original observation with two observations: one observation with Y=1 and a frequency weight = k(i), and a second observation with Y=0 and frequency weight = n(i)-k(i). I would also duplicate the x-values on each of the two observations. I would declare Y to be CATEGORICAL, and specify the analysis TYPE = LOGISTIC. Would that work? |
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Bob H posted on Thursday, June 10, 2004 - 10:37 pm
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In the last post, I should have said each observation has k(i) successes out of n(i) trials. |
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bmuthen posted on Friday, June 11, 2004 - 9:57 am
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Would be interesting if you could try this out on some known example. |
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bobh posted on Friday, June 11, 2004 - 11:14 am
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I just read in the Mplus User's Guide that frequency weights cannot be used when TYPE=LOGISTIC. |
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bmuthen posted on Friday, June 11, 2004 - 11:19 am
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But you don't need to use Type = Logistic to do this - you can simply request estimator = ml and then it will do logistic regression. That goes down a different track in Mplus which allows frequency weights. See the last paragraph in UG example 3.5 and the corresponding example on the Mplus CD where this is explicitly done. |
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Following up on the previous posts, is it possible to specify a binomial (n,p) distribution for variables in the latest version of Mplus? Thank you. |
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It is not possible to specify this distribution directly. I think however you can rearrange the data and use the binary input to estimate most models. In your data instead of the binomial variable use n binary variables some of them 0 and some of them 1 so that it corresponds to binomial count. If n varies across individual you can specify this as a binary univariate (long) twolevel model. You can also consider as an approximation the offset approach using Poisson distribution. See this thread http://www.statmodel.com/discussion/messages/23/781.html?1255011004 This approximation is theoretically solid when p is small, i.e., when p is small Poisson (np)=Binomial(n,p). By symmetry you can use that even when p is large. |
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I would like to create a CFA model with one factor and four count indicators. But each count indicator separately needs an offset correction for different exposure times (e.g. person m has another exposure time for y1 than for y2 etc.). So I have four count outcomes y1-y4 and four different log transformed exposure time variables ln1-ln4 (the Poisson regression coefficients for ln1-ln4 was fixed at 1). Is this model doable in Mplus in the following way: factor BY y1-y4*; factor@1; y1 ON ln1@1; y2 ON ln2@1; y3 ON ln3@1; y4 ON ln4@1; ! the 4 Intercepts are free parameters Thank you and best wishes for the new year! |
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Yes, this looks right. |
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I'm trying to compare the Mplus output of a ZIP model with the R output from PSCL. PSCL gives me this: Number of iterations in BFGS optimization: 13 Log-likelihood: -98.51 on 4 Df However, Mplus gives me this: Number of Free Parameters 3 Loglikelihood H0 Value -99.286 Can you tell me what accounts for the difference in the models? Thanks, Steve |
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Check that you have the same number of parameters. Sharpen the convergence criterion in Mplus using the mconvergence option. |
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