Logistic Regression Standard Error Of Prediction
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Logistic Regression Prediction Interval
of operation Announcements Customer service Register Stata online Change registration Change address Subscribe to Stata News Subscribe to email alerts International resellers Careers Our sites Statalist The Stata Blog Stata Press Stata Journal Advanced search Site index Purchase Products Training Support Company >> Home >> Resources & support >> FAQs >> Obtaining a standard error of the predicted probability This confidence interval logistic regression FAQ is for Stata 7 and older versions. Beginning in Stata 8, standard errors for predictions can be computed using predictnl. How do I obtain the standard error of the predicted probability with logistic regression analysis? Title Obtaining a standard error of the predicted probability with logistic regression analysis Author Roberto Gutierrez The predicted probability in a logistic regression is a transformation of the linear combination x^t beta. Thus, by the delta method, the predicted probability for H(t) = (1+exp(-t))^{-1} is pi = H(x^t beta) = H(linear combination) Applying the delta method, we get se(pi) = H'(linear combination) * stdp = pi*(1-pi)*stdp, by properties of the logistic function H(). Thus, to get standard errors for your predicted probabilities, the following sequence of commands will work nicely: . logit y x . predict p . predict stdp, stdp . gen se = p * (1-p) * stdp Stata New in Stata Why Stata? All features Features by disciplines Stata/MP Which Stata is right for me? Order Stata Shop Order Stata Bookstore Stata Press books Stata Journal Gift Shop Stat/Transfer Support Training Video tutorials FAQs Statalist: The
optionally, the estimated linear predictors and their standard error estimates, the estimates of the cumulative or individual response probabilities, and the confidence limits for the cumulative probabilities. Regression diagnostic statistics
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and estimates of cross validated response probabilities are also available for binary response covariance matrix models. If you specify more than one OUTPUT statement, only the last one is used. Formulas for the statistics are given in the sections Linear Predictor, Predicted Probability, and Confidence Limits and Regression Diagnostics, and, for conditional logistic regression, in the section Conditional Logistic Regression. If you use the single-trial syntax, the data http://www.stata.com/support/faqs/statistics/standard-error-predicted-probability/ set also contains a variable named _LEVEL_, which indicates the level of the response that the given row of output is referring to. For instance, the value of the cumulative probability variable is the probability that the response variable is as large as the corresponding value of _LEVEL_. For details, see the section OUT= Output Data Set in the OUTPUT Statement. The estimated linear predictor, its standard https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/statug_logistic_sect012.htm error estimate, all predicted probabilities, and the confidence limits for the cumulative probabilities are computed for all observations in which the explanatory variables have no missing values, even if the response is missing. By adding observations with missing response values to the input data set, you can compute these statistics for new observations or for settings of the explanatory variables not present in the data without affecting the model fit. Alternatively, the SCORE statement can be used to compute predicted probabilities and confidence intervals for new observations. Table 51.3 lists the available options, which can be specified after a slash (/). The statistic and diagnostic options specify the statistics to be included in the output data set and name the new variables that contain the statistics. If a STRATA statement is specified, only the PREDICTED=, DFBETAS=, and H= options are available; see the section Regression Diagnostic Details for details. Table 51.3 OUTPUT Statement Options Option Description ALPHA= specifies for the confidence intervals OUT= names the output data set Statistic Options LOWER= names the lower confidence limit PREDICTED= names the predicted probabilities PREDPROBS= requests the individual, cumulative, or cross validated predicted probabilities STDXBETA= names the standard error estimate of t
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 http://stackoverflow.com/questions/14423325/confidence-intervals-for-predictions-from-logistic-regression the company Business Learn more about hiring developers or posting ads with us Stack Overflow Questions Jobs Documentation Tags Users Badges Ask Question x Dismiss Join the Stack Overflow Community Stack Overflow is a community of 6.2 million programmers, just like you, helping each other. Join them; it only takes a minute: Sign up Confidence intervals for predictions from logistic regression up vote 37 down vote favorite 26 In R predict.lm computes predictions logistic regression based on the results from linear regression and also offers to compute confidence intervals for these predictions. According to the manual, these intervals are based on the error variance of fitting, but not on the error intervals of the coefficient. On the other hand predict.glm which computes predictions based on logistic and Poisson regression (amongst a few others) doesn't have an option for confidence intervals. And I even have a hard time logistic regression standard imagining how such confidence intervals could be computed to provide a meaningful insight for Poisson and logistic regression. Are there cases in which it is meaningful to provide confidence intervals for such predictions? How can they be interpreted? And what are the assumptions in these cases? r statistics glm confidence-interval share|improve this question asked Jan 20 '13 at 9:45 unique2 91211015 Maybe do it from the empirical distribution, that is, bootstrap the sample a couple of times and then you can compare your sample value against the empirical distribution. –PascalvKooten Jan 20 '13 at 10:19 1 confint() will give profile likelihood intervals on model terms, but the OP wants a prediction interval. IIRC there is no distinction between confidence and prediction intervals in the GLM. –Gavin Simpson Jan 20 '13 at 11:47 But what does that give you that the standard errors quoted in summary(mod) doesn't? predict.lm() use the model to give values of response for values of the predictors. It can give prediction and confidence intervals. In a GLM, IIRC, these are the same thing. Hence what I show in the answer is how to do what predict.lm() does but for a GLM, based only on standard errors of predictions. –Gavin Simpson Jan 20 '13 at 12:43 @A
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