# Questions tagged [logistic-regression]

For questions about logistic regressions, a regression model where the dependent variable is categorical.

140 questions
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### How to prove the logistic loss function is strongly convex?

The logistic loss function is: $$\mathcal{L}=\frac{1}{n}\sum_{i=1}^n\log(1+\exp(-y_ix_i^T\theta))$$ in which $y_i\in\{-1,+1\},x\in \mathbb{R}^d$. How to show that $\mathcal{L}$ is strongly convex. My ...
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### What type of analysis with binomial dependent variable that’s repeated

I can’t for the life of me figure out what type of analysis I need to run in SPSS and I am EXTREMELY statistically delayed so any responses in the most simplest explanation would be amazing. I had 14 ...
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### Formula for ordinal complementary log-log regression

I have a model developed in R using the polr() function in the MASS package. The model is an ordinal regression with a complementary log-log link (method=cloglog). The model uses four predictors ...
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### How is the log-likelihood for a multinomial logistic regression calculated?

In a multinomial logistic regression, the predicted probability $\pi$ of each outcome $j$ (in a total of $J$ possible outcomes) is given by: $\pi_j = \frac{e^{A_j}}{1+\sum_{g \neq j}^Je^{A_j}}$ ...
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### Finding population growth rate given initial population and average pubs per female reproduction

I am new to mathematical modeling and having trouble modelling the following population growth scenario: Starting population: $100$ individuals Average age: $7$ years Assumption: population equally ...
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### logistic regression without $L_2$-regularization does not have optimum?

I have a question related to machine learning. Consider the case when in the problem of binary classification the training set is linearly separable. How to show that in this case the optimization ...
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### How does one write the equation for a logit model, and then the odds ratio, with multiple explanatory variables?

I see logit equations always written with a single dependent variable, however I am running a logit model which outputs the coefficients for three explanatory variables (X1, X2, and X3) with respect ...
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### Fisher Matrix and Hessian matrix

I know that the Fisher matrix is easily obtained from the Hessian matrix $I\left(\hat{\beta}\right)=-H\left(\hat{\beta}\right)$ Why is the covariance variance matrix the inverse of the Fisher ...
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### how log likelihood's derivative is equal to zero in maximum log likelihood.

if the log-likelihood function is strictly increasing and it has not horizontal asymptote then how it's derivative is equal to zero in maximum log likelihood. Now since it is strictly increasing every ...
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### Odds Ratios with independent linear trends

I have a question regarding odds ratios for a project I'm working on. For my analysis to determine if there was a significant change in access to a service at a certain type of facility from one year ...
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### Bayesian Logistic Regression, conditional probability integration

In Andrew NG's Lectures (CS229), the Bayesian Logistic Regression section contained a formula; $$P(Y|X,S)=\int_\theta P(Y|X,\theta)P(\theta|S)d\theta$$ Here, $\theta$ is treated as a random variable....
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### How to select a threshold that penalize more on Type I error?

I am trying to do a binary classification in which Type I error is more important than Type I error. Which metric should I use to select the threshold value to penalize more on Type II error?
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### How to do prediction in a binary classification with logistic regression when we care much more about type I error than type II error?

How to do prediction in a binary classification with logistic regression when we care much more about type I error than type II error? Which criteria should I use to select the threshold value and ...