Logistic Regression Equation Error Term
Contents |
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 why is there no error term in logistic regression Learn more about Stack Overflow the company Business Learn more about hiring developers
Logistic Regression Error Distribution
or posting ads with us Cross Validated Questions Tags Users Badges Unanswered Ask Question _ Cross Validated is a question and logistic regression error variance 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 logit regression Anybody can answer The best answers are voted up and rise to the top Logistic Regression - Error Term and its Distribution up vote 12 down vote favorite 6 On whether an error term exists in logistic regression (and its assumed distribution), I have read in various places that: no error term exists the error term has a binomial distribution (in accordance with the distribution of the response
Simple Logistic Regression Example
variable) the error term has a logistic distribution Can someone please clarify? logistic binomial bernoulli-distribution share|improve this question edited Nov 20 '14 at 12:43 Frank Harrell 39.1k173156 asked Nov 20 '14 at 10:57 user61124 6314 4 With logistic regression - or indeed GLMs more generally - it's typically not useful to think in terms of the observation $y_i|\mathbf{x}$ as "mean + error". Better to think in terms of the conditional distribution. I wouldn't go so far as to say 'no error term exists' as 'it's just not helpful to think in those terms'. So I wouldn't so much say it's a choice between 1. or 2. as I would say it's generally better to say "none of the above". However, irrespective of the degree to which one might argue for "1." or "2.", though, "3." is definitely wrong. Where did you see that? –Glen_b♦ Nov 20 '14 at 13:52 @Glen_b: Might one argue for (2)? I've known people to say it but never to defend it when it's questioned. –Scortchi♦ Nov 20 '14 at 14:49 2 @Glen_b All three statements have constructive interpretations in which they are true. (3) is addressed at en.wikipedia.org/wiki/Logistic_distribution#Applications and en.wikipedia.org/wiki/Discrete_choice#Binary_Choice. –whuber♦ Nov
model Generalized linear model Discrete choice Logistic regression Multinomial logit Mixed logit Probit Multinomial probit Ordered logit logistic regression pdf Ordered probit Poisson Multilevel model Fixed effects Random effects logistic regression ppt Mixed model Nonlinear regression Nonparametric Semiparametric Robust Quantile Isotonic Principal components Least angle Local
Binary Logistic Regression Spss
Segmented Errors-in-variables Estimation Least squares Ordinary least squares Linear (math) Partial Total Generalized Weighted Non-linear Non-negative Iteratively reweighted Ridge regression Least absolute deviations Bayesian http://stats.stackexchange.com/questions/124818/logistic-regression-error-term-and-its-distribution Bayesian multivariate Background Regression model 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 function. In statistics, logistic regression, or logit regression, or logit https://en.wikipedia.org/wiki/Logistic_regression 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, 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 f
the performance of the model Why use logistic regression? There are many important research topics for which the dependent variable is "limited" (discrete not continuous). Researchers often want to analyze whether some http://www.appstate.edu/~whiteheadjc/service/logit/intro.htm event occurred or not, such as voting, participation in a public program, business success or failure, morbidity, mortality, a hurricane and etc. Binary logistic regression is a type of regression analysis where the dependent variable is a dummy variable (coded 0, 1). A data set appropriate for logistic regression might look like this: Descriptive Statistics Variable N Minimum Maximum Mean Std. Deviation YES 122 .00 1.00 logistic regression .6393 .4822 BAG 122 .00 7.00 1.5082 1.8464 COST 122 9.00 953.00 416.5492 285.4320 INCOME 122 5000.00 85000.00 38073.7705 18463.1274 Valid N (listwise) 122 *This data is from a U.S. Department of the Interior survey (conducted by U.S. Bureau of the Census) which looks at a yes/no response to a question about the "willingness to pay" higher travel costs for deer hunting trips in North Carolina logistic regression error (a more complete description of this data can be found here). The linear probability model "Why shouldn't I just use ordinary least squares?" Good question. Consider the linear probability (LP) model: Y = a + BX + e where Y is a dummy dependent variable, =1 if event happens, =0 if event doesn't happen, a is the coefficient on the constant term, B is the coefficient(s) on the independent variable(s), X is the independent variable(s), and e is the error term. Use of the LP model generally gives you the correct answers in terms of the sign and significance level of the coefficients. The predicted probabilities from the model are usually where we run into trouble. There are 3 problems with using the LP model: The error terms are heteroskedastic (heteroskedasticity occurs when the variance of the dependent variable is different with different values of the independent variables): var(e)= p(1-p), where p is the probability that EVENT=1. Since P depends on X the "classical regression assumption" that the error term does not depend on the Xs is violated. e is not normally distributed because P takes on only two values, violating another "classical regression assumption" The predicted