Error Error In Computing Inverse Link Function
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How Do You Find The Inverse Of A Function
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Proc Genmod Error In Parameter Estimate Covariance Computation
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define your own link functions and response probability distributions by using the FWDLINK, INVLINK, VARIANCE, and DEVIANCE statements. The variables assigned in these statements can have values computed in programming statements. These programming statements can occur anywhere between the PROC GENMOD statement and the RUN statement. Variable names used in programming statements must be unique. Variables from the input data set can be referenced in programming statements. The mean, linear predictor, and response are represented by the automatic variables _MEAN_, _XBETA_, and _RESP_, respectively, which can be referenced in your programming statements. Programming statements are used to define the functional https://communities.sas.com/t5/SAS-Statistical-Procedures/Proc-genmod-how-to-resolve-error-messages/td-p/33607 dependencies of the link function, the inverse link function, the variance function, and the deviance function on the mean, linear predictor, and response variable. The following statements illustrate the use of programming statements. Even though you usually request the Poisson distribution by specifying DIST=POISSON as a MODEL statement option, you can define the variance and deviance functions for the Poisson distribution by using the VARIANCE and DEVIANCE statements. https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/statug_genmod_sect024.htm For example, the following statements perform the same analysis as the Poisson regression example in the section Getting Started: GENMOD Procedure. The statements must be in logical order for computation, just as in a DATA step. proc genmod ; class car age; a = _MEAN_; y = _RESP_; d = 2 * ( y * log( y / a ) - ( y - a ) ); variance var = a; deviance dev = d; model c = car age / link = log offset = ln; run; The variables var and dev are dummy variables used internally by the procedure to identify the variance and deviance functions. Any valid SAS variable names can be used. Similarly, the log link function and its inverse could be defined with the FWDLINK and INVLINK statements, as follows: fwdlink link = log(_MEAN_); invlink ilink = exp(_XBETA_); These statements are for illustration, and they work well for most Poisson regression problems. If, however, in the iterative fitting process, the mean parameter becomes too close to 0, or a 0 response value occurs, an error condition occurs when the procedure attempts to evaluate the log function. You can circumvent this kind of problem by u
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Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What are the error distribution and link functions of a model family in R? up vote 4 down vote favorite 1 When building models with the glm function in R, one needs to specify the family. A family specifies an error distribution (or variance) function and a link function. For example, when I perform a logistic regression, I use the binomial(link = "logit") family. What are (or represent) the error distribution (or variance) and link function in R ? I assume that the link function is the type of model built (hence why using the logit function for the logistic regression. But I am not too sure about the error distribution function. I had a look at R's documentation but could not find detailed information other than how to use them and what parameters can be specified. r distributions generalized-linear-model variance link-function share|improve this question edited May 13 at 21:58 asked May 13 at 17:17 user5365075 233 en.wikipedia.org/wiki/Generalized_linear_model#Link_function –Sycorax May 13 at 17:37 1 Your question isn't so much to do with R but to do with generalized linear modes more generally. –Glen_b♦ May 13 at 17:49 add a comment| 2 Answers 2 active oldest votes up vote 4 down vote accepted You don't specify the "error" distribution, you specify the conditional distribution of the response. When you type the name of the family (such as binomial) that specifies the conditional distribution to be binomial, and that implies that the variance function is $\mu(1-\mu)$. If you choose a different family you get a different variance function (for Poisson it's $\mu$, for Gamma it's $\mu^2$, for Gaussian it's constant, for inverse Gaussian its $\mu^3$, and so on). [For some cases (e.g. logistic regression) you can take a latent-variable approach to the GLM - and in that case, you might possibly regard the distribution of the latent variable as a form of "error distribution".] The link function determines how the mean ($\mu$) and the linear predictor ($\eta=X\beta$)