Logistic Regression Error Variance
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Logistic Regression Model
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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 Error distribution for linear and logistic regression up vote 4 down vote favorite 2 With continuous data, a linear regression $Y=\beta_1+\beta_2X_2+u$ assumes that the error term is distributed N(0,$\sigma^2$) 1) Do we assume that Var(Y|x) is likewise ~N(0,$\sigma^2$)? 2) logistic regression assumptions What is this error distribution in logistic regression? When the data is in the form of 1 record per case, where the "Y" is 1 or 0, is the error term distributed Bernoulli (i.e. variance is p(1-p) )) and when the data is in the form #successes out of #of trials, is it assumed binomial (i.e. variance is np(1-p)), where p is the probability that Y is 1? logistic generalized-linear-model share|improve this question edited Nov 20 '14 at 13:53 Scortchi♦ 18.5k63370 asked Sep 22 '12 at 1:34 B_Miner 1,03834177 1 You are not being precise.The model assumption is that the error terms are independent and identically distributed with a distribution that is N(0,σ$^2$) and is unrelated to the COVARIATE. What is Var(Y|x)? Are you conditioning on X$_2$ =x? Does the model assume the covariate is random in some way or so we assume that the covariate is fixed according to a design matrix? I think it is the latter and therefore Var(Y|X$_2$=x) is implied by the assumptions and does not need to be assumed. –Michael Chernick Sep 22 '12 at 3:28 @MichaelChernick Why does
model Generalized linear model Discrete choice Logistic regression Multinomial logit Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson Multilevel model Fixed effects Random effects Mixed model Nonlinear regression Nonparametric Semiparametric Robust Quantile Isotonic Principal
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components Least angle Local Segmented Errors-in-variables Estimation Least squares Ordinary least squares Linear logistic distribution (math) Partial Total Generalized Weighted Non-linear Non-negative Iteratively reweighted Ridge regression Least absolute deviations Bayesian Bayesian multivariate Background Regression model logistic function validation Mean and predicted response Errors and residuals Goodness of fit Studentized residual Gauss–Markov theorem Statistics portal v t e "Logit model" redirects here. It is not to be confused with Logit http://stats.stackexchange.com/questions/37776/error-distribution-for-linear-and-logistic-regression function. In statistics, logistic regression, or logit regression, or logit model[1] is a regression model where the dependent variable (DV) is categorical. This article covers the case of binary dependent variables—that is, where it can take only two values, such as pass/fail, win/lose, alive/dead or healthy/sick. Cases with more than two categories are referred to as multinomial logistic regression, or, if the multiple categories are ordered, https://en.wikipedia.org/wiki/Logistic_regression as ordinal logistic regression.[2] Logistic regression was developed by statistician David Cox in 1958.[2][3] The binary logistic model is used to estimate the probability of a binary response based on one or more predictor (or independent) variables (features). As such it is not a classification method. It could be called a qualitative response/discrete choice model in the terminology of economics. Logistic regression measures the relationship between the categorical dependent variable and one or more independent variables by estimating probabilities using a logistic function, which is the cumulative logistic distribution. Thus, it treats the same set of problems as probit regression using similar techniques, with the latter using a cumulative normal distribution curve instead. Equivalently, in the latent variable interpretations of these two methods, the first assumes a standard logistic distribution of errors and the second a standard normal distribution of errors.[citation needed] Logistic regression can be seen as a special case of the generalized linear model and thus analogous to linear regression. The model of logistic regression, however, is based on quite different assumptions (about the relationship between dependent and independent variables) from those of linear regression. In particular the key differences of these two m
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