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Questions tagged [logistic-curve]

A common S-shaped ("sigmoid") curve, defined as $f(x) = L/(1+e^{-k(x-x_0)})$.

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1answer
33 views

Generate odds ratios across deciles / quantiles of an indpendent variable

With reference to the following figure from Bellomo et al., 2011: How exactly are the odds ratios across the deciles 'referenced against the 4th decile' calculated? My initial impression is that a ...
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0answers
32 views

derivative of cross entropy yields log-odds, does that make sense?

I am looking for a proof how to derive the logistic regression from cross-entropy loss, i.e. derive the form of a sigmoid from cross entropy. my thoughts are these: $\ell = y_i \ln{p_i} + (1-y_i)\ln{...
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2answers
180 views

Does the “divide by 4 rule” give the upper bound marginal effect?

In the logisitic regression chapter of "Data Analysis Using Regression and Multilevel/Hierarchical Models" by Gelman and Hill, The "Divide by 4" rule is presented to approximate average marginal ...
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48 views

How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ for the logistic distribution?

Take the distribution function $\Phi(z) = \frac{1}{1+\exp(-z)}$ and density function $\phi(z)=\Phi(z)(1-\Phi(z))$ of the logistic distribution. How can one calculate the integral below? $$\...
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1answer
42 views

How to treat block (IV) in glm?

I have a word learning experiment in which I am measuring accuracy on a 2AFC task. So, my DV is binary (1=correct, 0=incorrect). As IVs I have ...
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3answers
37 views

Two logistic regression or one Softmax regression

The following question is from Geron's Hans-On Machine Learning book. Suppose you want to classify pictures as outdoor/indoor and daytime/nighttime. Should you use two Logistic regression or one ...
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36 views

Logistic Regression For Classification [duplicate]

The origin of logistic regression is actually logistic curve which varies from the value 0 to the value 1. It looks like the letter S, and it specifies the growth of species. If our data distribution ...
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2answers
93 views

How to explain the utility of binomial logistic regression when the predictors are purely categorical

The resources that I have seen feature graphs such as the following This is fine if the predictor $x$ is continuous, but if the predictor is categorical and just has a few levels it's not clear to ...
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1answer
24 views

Inverted dose-response variables

Context: Often when we carry out dose-response modelling we want to estimate the dose required to elicit a predetermined response (i.e. response ~ dose). Typically this is done with inverse ...
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1answer
68 views

I am making a logistic regression model. Should I test for multicollinearity in dependent features if my predicting feature in categorical?

I have a doubt, will multicollinearity affect my Logistic Regression model as my predicting(output) feature is categorical? (because correlation will make sense only for 2 continuous features and not ...
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1answer
300 views

Logistic regression not producing an s-shaped curve

I am trying to create a model that shows on the y axis a range from 0-1 and get that distinctive binary dependent variable s-shaped curve, yet I am not able to get it with the following code. ...
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2answers
137 views

How to combine properties of different functions into a new function?

The logistic function has the differential equation: dy / dt = ky(1 - (y / L)) Solving this differential equation by separation of variables and integration yields the Logistic Equation: f(t) = L / ...
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117 views

Fitting a logistic growth curve with an iterative formula in R

I'm trying to fit a logistic growth curve to specific countries GDP data using an equation, $P_{n+1} = rP_n(1-\frac {P_n}{k})$. (1) I've found constants $r$ and $k$ simply by finding a ...
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0answers
109 views

Approximation or closed form equation for summation of logistic function [closed]

The spread of epidemics follows a logistic growth, given in the equation below $I(t) = \frac{N}{1+(N-1)exp^{-rNt}}$ where, N is the population size, r is infection rate, t is time , I(t) is ...
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1answer
54 views

importance sampling strategies

I am trying to approximate the expectation of the "complete-data likelihood" with respect to the distribution of some missing data, and I am having some trouble. This expectation can be written as $$ ...
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0answers
41 views

How to refine a logistics population model? [closed]

I have to refine a logistic population model so that it more accurately fits a set of data and was wondering how to do this. The only way I can find is to use a variable carrying capacity however I ...
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1answer
58 views

Derivation Harvey (1984) Logistic Curve

Given a logistic function of the form. \begin{align*} f(t) = \frac{\alpha}{1 + \beta e^{\gamma t}} \end{align*} Harvey (1984) differentiates this and takes logs to yield: \begin{align*} \ln f' = 2 ...
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1answer
1k views

Why do we use logistic regression for classification problems, rather than other continuous functions? [duplicate]

I understand that logistic regression has some nice properties that works well for classification problems, such as the S-curve shape, the output value being between [0,1], and continuous across X. ...
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1answer
382 views

Why sigmoid function in logistic regresion can make good estimations on non-linear data?

If I understood correctly, then in the logistic regression we select the parameters of the sigmoid function so that it maximally approximates the input data. I can understand why logistic regression ...
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114 views

Plotting the results of a logistic regression

I ran a logistic regression in R and then I went to plot it and I'm not sure how to understand the plot. Here's the logistic regression - ...
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0answers
48 views

Hierarchal Bayes: logistic regression

We have the following model that was proposed to me. It takes yes, no and maybe responses to try and predict attendance $y_{i}$. $$ \begin{align} y_i &\sim \mathsf{Bin}(n, p_i) \\ p_i &= \...
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1answer
1k views

How to compare logistic regression curves?

I have a binary dependent variable whose probability depends on a continuous independent variable, i.e., age. I have fit these into a logistic regression model and have the coefficients for the same. ...
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1answer
51 views

Finding the center of a logistic curve

Given a sigmoidal/logistic curve p what's the general procedure to finding at what value of x is the curve centered?
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0answers
108 views

Logistic regression, use of lagged indicator counts as explanatory variable

I am an intern and new to make sas scorecard model. A former colleague tells me that, when selecting features for a logistic regression model, you better not choose ones that are related to the past ...
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2answers
4k views

How to model positive S-shaped-function? [closed]

I need to transform my data into a function shown below. My data should fit in the range from 0 to 1. The inflection point should be on 0.5. How I can do this mathematically? Is there any similar ...
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3answers
467 views

Why $\log(\frac{p}{1-p}) = b_0+b_1x $ in Logistic regression

I have read about logistic regression on Quora and also from different online source and they said that, $$logit = b_0+b_1x$$ Where $logit = \log(\frac{p}{1-p}) = \log (\frac{probability-of-event-...
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1answer
79 views

How to calculate an index value between 1 and 0 for distance, based on a logistic function

I work with spatial ecology, and have calculated distances from one island to its neighboring islands. I want to transform these distances to index values between 0 and 1, where the closest islands ...
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1answer
196 views

Correlation of the sigmoid function of normal random varaibles

Suppose $X=(X_1,X_2)^T \sim N(\mu, \Sigma)$ and $p=(p_1,p_2)^T = (e^{X_1}/(1+e^{X_1}),e^{X_2}/(1+e^{X_2}))^T$. $Cov(X_1,X_2)=\sigma_{12}$. Does the following hold ? $\sigma_{12}=0 \Leftrightarrow ...
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2answers
230 views

What is the difference between a logistic curve and something that overshoots?

In population dynamics, the growth of a population can have exponential growth, or a logistic curve growth up to its carrying capacity, or it can overshoot the carrying capacity and fluctuate before ...
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0answers
303 views

Fitting of logit using least squares [duplicate]

So I am asked to fit a logit model using the method of least squares in connection to logistic regression. Let $\pi(x)=\mathrm{P}(Y=1|X=x)$ be the probability of success of a binary response variable $...
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1answer
1k views

Adjusting S-Curves (Sigmoid Functions) with Hyperparameters

I can define the sigmoid function in R with: ...
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1answer
145 views

How to analyse growth rate in R?

Within the framework of an experiment I followed to growth rate of bird nestlings. I measured them every day for weight and tarsus. I have a number of continuous and categorical explanatory variables, ...
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2answers
1k views

Fitting a dose response curve to 3 dose points

I have dose-response data sets, of 3 doses, 3 replicates for each dose. I'd like to fit a curve for these data sets and I'm mainly interested in the slope of the curve since I want to be able and ...
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2answers
308 views

(How) Can I fit a dataset with some parameters fit globally?

I want to fit some sigmoidal curves that follow the following equation: bottom+(top-bottom)/(1+10**((logIC50-x)*HillSlope)) the parameters top and bottom should ...
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1answer
400 views

Automatically finding starting values for a sigmoid curve

I have ~10.000 of vectors and I want to fit a sigmoid curve to each of them; in each case, I need to define starting parameters for fitting, so I want to find these parameters automatically. On ...
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7answers
11k views

Looking for function to fit sigmoid-like curve

I'm looking for a function to fit sigmoid-like curves, from experimental data points. The model (the function) doesn't matter, it doesn't have to be physically relevant, I just want to be able to ...
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3answers
2k views

Why is the logistic distribution called “logistic”?

What is "logistic" about the logistic distribution, in a common sense way? What is the etymology of and the lexical rationale for the name, not just pure math definition?
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0answers
891 views

Fitting a logistic curve to cumulative data using glm()

I'm trying to fit a logistic curve to cumulative data, derived from satellite imagery. Previously, I have point observation data which were either 0s or 1s. Os being 'forest' and 1s being 'non-forest'....
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1answer
174 views

Which steps have to be done before fitting logistic curve to time-series?

I want to cluster time-series concerning sales of products. In the database I have 26weeks after launching each products and units sold each week. One of the method of clustering is to cluster ...
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0answers
63 views

Fitting Inspection Time Data to Curve

I have a set of Inspection Time data that consists of two variables: SOA (stimulus onset asynchrony) and Accuracy. This data refers to how accurately you can perform on a simple stimuli ...
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1answer
2k views

Estimating the slope of the straight portion of a sigmoid curve

I have been given this task and was stumped. A colleague asked me to estimate the $x_{upper}$ and $x_{lower}$ of the following chart: The curve is actually a cumulative distribution, and x is some ...
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1answer
12k views

Maximum Likelihood Curve/Model Fitting in Python

I have some 2d data that I believe is best fit by a sigmoid function. I can do the fitting with the following python code snippet. ...
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2answers
17k views

What's the most pain-free way to fit logistic growth curves in R?

This isn't as easy to Google as some other things as, to be clear, I'm not talking about logistic regression in the sense of using regression to predict categorical variables. I'm talking about ...