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Questions tagged [logistic-regression]

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

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What do the parameters of a multinomial logistic regression correspond to?

I've recently started learning about data science/statistics and learned how to derive such models as linear regressors and logistic regressors. What I don't understand, however, is what the ...
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Vehicle Routing Problem that minimizes Total Time instead of Total Cost, with a few alterations

A company has to collect waste for different customers, at different locations, using two vehicles both with a certain capacity. The vehicles have to begin and end at the depot and when the capacity ...
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Is there a nice matrix expression for the gradient of the cross-entropy for multinomial logistic regression?

Does the gradient of the cross-entropy have a nice matrix expression? Let $\mathbf X$ be a matrix whose row vectors are features, and $$\mathbf Y_{ij} = \begin{cases} 1 & \text{if the $j$th row ...
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Distribution of logistic regression estimators

It is well known that for OLS estimators, the parameters are asymptotically normal, i.e. for the regression $y_i = \beta_i x_i$, $$\hat{\beta_i} \sim \mathcal{N}(\beta_i, \sigma^2 (X_i^T X_i)^{-1})$$ ...
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275 views

Sum of Sigmoid of Normal distribution

I have: $$p_{\text{sigmoid}_i} =\frac{e^{a+b{x_i}}}{1+e^{a+b{x_i}}}$$ where $x_1, \ldots, x_n$'s are generated from a normal distirbution with mean $\mu_0$ and $x_{n+1},\ldots,x_{2n}$ are generated ...
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Using Linear Regression for Classification

I am using Vowpal Wabiit to explore the power of different loss functions (e.g. squared, hinge, logistic, quantile) for classification. I've trained different models using each of these loss functions....
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A “softmax”-like function for deciding on a partition

Softmax can be derived as follows. Say that we are given $k$ "log priors" $b_i$ that our data belongs to the $i$th category in some categorical distribution. Then we can solve for the category ...
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Can anyone help with the inverse problem and tuning parameters

For my final year project i want to model the population of London using the Verhulst logistic model. However, to gain more marks i wish to use the inverse problem to tune the parameters to make the ...
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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 ...
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In logistic regression: What is the proper way to report the overall “odds ratios” for a non-linear continuous variable

I am fitting a logistic regression with multiple binary variables as well as a single continuous variable (AGE) for which I have a linear and a quadratic term. $$\log\frac P{1-P} = \text{constant} + ...
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Logistic Regression Coefficients transformation?

I have 5 columns of data. Column of lists_1, Total_1 which is a constant, column of lists_2 and Total_2 as a constant. Like this: ...
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Growth with restrictions (finding maxvalue of constant term)

I have the following differencial ekvation that shows the population change for fish, where x is a constant death rate by accident. How can I determine the maximum value of x so that the fish ...
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Expectation of Log Sum Dirichlet Random variables and Inference in Logistic Regression

Given $\mathbf{X}\sim\mathsf{Dir}(\alpha_1,\cdots,\alpha_k)$, is there an expression for the expectation $$ \mathbb{E}\left[ \log \left(\mathbf{c}^\top \mathbf{X} \right)\right] $$ where $\mathbf{c}\...
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Pearson Residual Calculation for Logistic Regression in SAS

I am currently reading through the third edition of Applied Logistic Regression by David Hosmer, Jr., Stanley Lemeshow, and Rodney Sturdivant, and I'm on the section regarding logistic regression ...
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47 views

Updating weight based on fisher scoring algorithm [wikipedia]

My understanding on weight update for fisher is based on wikipedia description. The fisher information is said as the expectation of hessian. Can someone explain how is the expection for each entry of ...
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58 views

Approximate order statistics for Half-normal probability plot

To construct the half-normal probability plot, plot the absolute values in a certain statistical diagnostic (residual, leverage, Cook distance and others) versus $z_i$ where: $\displaystyle z_{i} = \...
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144 views

logistic regression global maximum

I am uncertain if this is the case both in general (does logistic regression always find global optimum) and in particular (does logistic regression always find global optimum when that the ...
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177 views

Best optimization method for minimizing error of estimated default probability

The credit risk modelling problem can be stated as: $$ \min_{a \in \mathbb{R}^{1 \times n}} \sum_i \Big( d_i -\frac{\exp(a x_i) }{1+\exp(a x_i)}\Big)^2 $$ Where $ d_i \in \mathbb{N} \in [0,1] $ is the ...
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26 views

Adjustement in logistic regression model

Hi everyone I am dealing with a tricky situation. I will try to explain quickly my problem. I am working with a tool comprise of 7 items. Each item have 3 status ( bad, medium and good). In my study ...
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19 views

How to distort a sigmoid / logistic function?

Please help. I need to move an object such that its distance / time profile resembles a sigmoid curve but in a non-symmetrical manner. 1- Let's say that I need to move 800cm in 3 seconds. How do I ...
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22 views

For a Maximum Likelihood Estimation with events that implicate each other, how should the likelihood function be constructed?

The probability of a student with a skill parameter of "s" to obtain at least a score of "k" in a certain test is defined as: $$\frac{1}{e^{b_k-s}+1}$$ Where $b_k$ is a difficulty parameter of ...
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Integral of logistic normal distribution approximation

Following paper about Glicko rating have a expression below: Parameter estimation in large dynamic paired comparison experiments (Equation 18, 19 on Appendix A) $$ \int \frac{ (10^{(\theta-\theta_j)...
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71 views

Minimum sufficient statistic for logistic regression model

For the question in the link below, I am seeking the minimal sufficient statistic for $\theta$={$\beta_1$,$\beta_2$} in the linear regression model given. I have taken the ratio of likelihoods $...
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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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61 views

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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41 views

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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39 views

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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14 views

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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101 views

Why Sigmoid function is so popular in every field of science?

I don't know if this is a silly question but still I couldn't resist my self from asking this. I recently came to know about the standard sigmoid function while learning about logistic regression ...
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33 views

Loss function : finding the criterion for which a given solution is the optimal classifier

For a binary classification problem, let $\eta(x) = P[Y=1 \mid x],$ and, for a given classifier $g$, we define the asymmetric cost : $$ L(g) = P[g(X)=0, Y=1] +\lambda P[g(X)=1,Y=0]$$ For this cost, ...
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Solving a logistic regression problem with my calculator gives “singular matrix” error. Why?

In my homework, I was given the following problem: The following data represent the population of a country. An ecologist is interested in building a model that describes the population. $$\...
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Is a Logistic Regression always viable for having a dichotomous response variable?

Yes, I've asked this question already on stat.stackexchange, but I'm asking here as well to see if I can get any other feedback on the subject I have learned some about a simple logistic regression ...
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Can I view maximum likelihood as finding the closest probability mass function (pmf) to the pmf with all its mass on the observed value

I took a deep dive into logistic regression recently. I was bothered by the fact that the likelihood formula often explicitly incorporates the values of the coding (0 or 1) into the calculation. In ...
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How should I calculate cost function based on SSE and Sigmoid values?

Given the following Samples: x1 : X= 80, y =1, x2: X=20, y =1 , and x3: X = 120 y = 0 How should i go about these questions ? 1) Calculate the probability that y = 1 for each 𝑥0 of the data set (h𝜽...
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Equivalent Neural Network in Keras to Multinomial Logistic Regression Using VGG16 Bottleneck features

In the Kaggle Dog Breed Identification kernel: https://www.kaggle.com/gaborfodor/dog-breed-pretrained-keras-models-lb-0-3 The bottleneck features from the VGG16 model (using Keras) are feed into a ...
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Which bivariate analysis to use for determining significance in predictors between two groups?

I'm conducting a "typical" statistical analysis in my research, but I have a few questions regarding appropriateness of the tests I'm using and whether or not I'm doing things the correct way. I don't ...
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Logistical Curve Tansformations

Mostly I am having a brain fart. Working on a game and wanted to use logistical curve for the experiance gain of skill levels. Idea is to create a system the reflects natural learning; early on you ...
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softmax function in logistic regression: confusion about two different forms

I read that, in multiclass logistic regression, we have a pivot class $K$ and $K-1$ set of $\vec{w}$ weights, then, for the pivot class: \begin{eqnarray} P( C_K | \vec{x} ) &= 1- \sum_\limits{t=...
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How to get the closed form of integration of sigmoid function multiply normal distribution density function

As the title describes, I want to get the closed form of the following equation $$ f(\sigma,\mu) = \int_{-\infty}^{\infty} \frac{1}{1+e^{-(\beta X + \alpha)}}\frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(X-\...
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Do logistic functions have to be symmetrical?

I'm attempting the find the equation of a graph i have plotted, which is S shaped similar to a logistic function. I want to use the logistic function equation to model it, but "top curve" of the S is ...
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Convex optimization when the min is minus infinity

I am new to convex optimization and I understand that when the function is convex, it is very easy to find the minimum since no matter where we start, we will always go down to the minimum. But what ...
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335 views

Logistic regression of large dataset

I need to build a logistic regression model to do some predictions. However, the dataset is very large, consisting of about 500,000 rows. For example, if we are going to build a model on whether ...
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Hessian of the logistic regression cost function

I am trying to find the Hessian of the following cost function for the logistic regression: $$ J(\theta) = \frac{1}{m}\sum_{i=1}^{m}\log(1+\exp(-y^{(i)}\theta^{T}x^{(i)}) $$ I intend to use this to ...
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Logistic regression with arbitrary labels

I am doing logistic regression on some team stats for March Madness, where my response is 1 if "team A wins" and 0 if "team A loses". The problem with that is that the label "team A" is arbitrary. ...
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209 views

Why can the logit function be written as a linear function?

The logit function is $ ln \frac{F(x)}{1-F(x)} $. According to wikipedia and the variety of materials that I have read, we can write this in linear form ($\beta_0 + \beta_1x$) for purposes of ...
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Model for headphone quality as a function of price

I've looked for any mathematical model that shows headphone quality as a function of the price of the headphones, but have not found anything yet. Of course, "quality" is quite subjective, which could ...
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46 views

how to use original dataset to get the logistic regression?

This from wikipedia https://en.wikipedia.org/wiki/Logistic_regression I understand P(X=2)=0.26 is the predicted probability when hours is 2 after the logistic regression. I want to know how do we use ...
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Predict the probabilty of a value belonging to a particular class

I have got two classes : BG and FG and a set of values assigned to each of these classes. Given a new value how can I find ...
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47 views

Linear regression where explanatory variable of 0 has no meaning

I want to build a predictive model, where given a few numeric explanatory variable n1, n2, n3...