Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [logistic-curve]

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

58 questions
24
votes
2 answers

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 fitting a logistic growth curve to given data points.…
readyready15728
  • 417
  • 1
  • 3
  • 13
24
votes
3 answers

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?
Multifix
  • 343
  • 3
  • 7
11
votes
1 answer

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 kind of measurements. He is interested to know what…
Penguin_Knight
  • 11,078
  • 29
  • 48
9
votes
2 answers

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 effects. Essentially, dividing the estimated log-odds…
Michael Webb
  • 1,936
  • 10
  • 21
7
votes
2 answers

Confidence Intervals for the Parameters of a Logistic Growth Curve

I'm using the growthcurver library to estimate the parameters from some bacterial growth curves. It fits a logistic equation of the following form: This returns values for K, N0 and r in that equation, along with standard errors. I would like,…
Fomite
  • 21,264
  • 10
  • 78
  • 137
7
votes
7 answers

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 calculate y from any x. And I don't want to…
Rififi
  • 315
  • 2
  • 3
  • 8
6
votes
1 answer

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. from scipy.optimize import curve_fit ydata = array([0.1,0.15,0.2,0.3,0.7,0.8,0.9, 0.9, 0.95]) xdata =…
Nick Crawford
  • 363
  • 1
  • 3
  • 7
6
votes
1 answer

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, as well as brood ID that should be used as a…
user3162369
  • 126
  • 6
5
votes
1 answer

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. The problem is that I have 3 such curves (for 3…
Polisetty
  • 217
  • 4
  • 15
4
votes
1 answer

What is $\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$ for $c\in\mathbb{R}$

It is straightforward to show $$\int_{-\infty}^{\infty}\Phi(a+bx) \phi( x ) dx = \Phi\left(\frac{a}{\sqrt{1+b^2}}\right)$$ but what value does $$\int_{c}^{\infty}\Phi(a+bx) \phi( x ) dx$$ have for $c<\infty$, e.g., for $c=0$? Even a good…
Jenny Reininger
  • 244
  • 1
  • 7
4
votes
2 answers

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 eventually settling down at the carrying capacity.…
HumbleOrange
  • 449
  • 2
  • 6
3
votes
1 answer

Decision boundary of logistic Regression and Hypothesis space in R

I am trying to generate a decision boundary of logistic regression. My Training set is 2/3 and the test set is 1/3, I have however tried producing the decision boundary but not sure whether is it the desired behavior or not. I am using the caret…
Ranji Raj
  • 259
  • 1
  • 6
3
votes
1 answer

Logistic probabilities of state variable in a hidden Markov model always has variance of zero

Here is a simplified version of a more complicated problem that I have. Imagine a hidden Markov model where the state is $X_t\sim N(\mu,\sigma^2)$. The observed variable is $Y_t\sim Bin(N, p_t)$ where $N$ is fixed and $p_t$ is a logistic map of the…
squipbar
  • 81
  • 4
3
votes
1 answer

How to fit a piecewise assembly of nonlinear functions?

I am trying to model vegetation spectral signatures (grey lines) using a two-part piecewise function (black dotted lines). In it, I am trying to use only a few points (red dots) to fit a linear (first part) and logistic function (second…
Gustavo
  • 51
  • 3
3
votes
2 answers

What is the interpretation of the "C" parameter in the five parameters logistic curve?

I'm using the following equation for the 5-parameters logistic curve: $$ y = A + \frac{D-A}{\Bigl(1+\exp\bigl(B(C-x)\bigr)\Bigr)^S} $$ What is the interpretation of the $C$ parameter? I found some docs which say that it corresponds to the inflection…
Stéphane Laurent
  • 17,425
  • 5
  • 59
  • 101
1
2 3 4