Questions tagged [nonlinear-regression]

Use this tag only for regression models in which the response is a nonlinear function of the parameters. Do not use this tag for nonlinear data transformation.

Nonlinear regression concerns models that are inherently nonlinear: that is, they cannot be expressed as a linear combination of parameters $\beta$. It is practically the same thing to say that a nonlinear model cannot be put into the form $Y = X\beta + \epsilon$ after a preliminary mathematical re-expression of $X$, $Y$, or both. For example, $Y = \log(X)\beta + \epsilon$ and $Y = \exp(X\beta + \epsilon)$ are both linear whereas $Y = exp(X\beta) + \epsilon$ and $Y = \log(X + \beta) + \epsilon$ are nonlinear.

(As usual, $Y$ is a dependent variable (or vector thereof), $X$ is a vector of independent variables, $\beta$ is a set of parameters to be estimated, and $\epsilon$ is random "error" with zero mean.)

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Estimating effect of latent variable in regression

I believe that independent variables $X_1,X_2$ affect the dependent variable $Y$ through a latent variable $Z$ such that $$ \begin{align} Y &= \beta_0 + \beta_1Z \\ Z &= \operatorname{Logit}^{-1}(\beta_2X_1 + \beta_3X_2) \\ \\ Y &= \beta_0 +…
fgregg
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Reconciling different parameterizations of the same nonlinear model

a journal article has a method for designing experiments to be fit to a 4-parameter logistic model. The model used is $y= D + \frac{A - D}{1 + (\frac{x}{C}) ^ B}$ A = upper asymptote B = maximum slope C = x value when y = 50% of maximum (i.e. 1/2…
Paul
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Best functional form to describe a scatterplot with a z-shape appearance with noise

What might be the general form of the equation can be fitted to the below scatter plot? The result should look like an smooth Z
K-1
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Polynomial regression as equation for a paper

I need to write the following model in equation form for a paper: Is the following equation describing the model correctly? Edit: I forgot to mention that this is a machine learning model. The purpose of the equation is simply to state it in the…
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Sequential problem for n=1, non linear regression

I am trying to understand an example in my stats course notes, the example relates to calculating the best value for the next experiment. The function of the line is very simple: $$\ln(Y_i) = \ln(\theta^*_1 + \theta^*_2x_i) + \epsilon_i$$ The…
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How to compare results obtained by non-linear regression

I have been using non-linear regression to analyze binding between two biomolecules. Each individual experiment was done in triplicate. The average of these triplicate values (with associated error) were analyzed using regression ([L]=known). …
Stylize
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Formulating and fitting a nonlinear model that looks like a product of linear models

I've got a dataset that I'd like to model, and it seems like the best model would be of the form: $y = (\beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3) \cdot (\beta_4 x_4 + \beta_5 x_5 + \beta_6 x_6) + \epsilon$. The $\beta_4$ through $\beta_6$ are…
Harlan
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How to measure the degree of nonlinearity in regression model

Could anyone guide me on how can we measure the curvature of nonlinear models? I have to know the methodology to measure nonlinearity (both intrinsic and parametric) for nonlinear regression model. For example, if we have the nonlinear model y =…
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Error on extrapolated values from a fitted function

I have some data points and I fitted a function (2nd order polynomial here) to the data. The algorithm (scipy.optimize.curve_fit) gave me the optimal parameters and the covariance matrix of those parameters. In the documentation, it says that the…
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Nonlinear Random Effects Model Specification in R

I have a dependent variable w with independent variable x representing time, which is clustered by variable site. In addition, I have indicator variables for 3 time period: i1, i2, i3, which correspond to three distinct time periods along the…
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Specific type of dummy regression

I would like to regress the values on the y-axis by the values of the x-axis. As you can see, the relationship is not linear. Values of y are only positive can not exceed 4, values of x are always positive. Is it possible (and do you think it is a…
Kasper
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Where to start with nonlinear regression?

What are some good introductory materials for learning non-linear regression modeling? Bonus points for anything freely available. Thanks!
Robb
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Non-Linear Relationship for a Log-Log Model

I currently have a log-log model. Its scatter plot looks like this: I am currently stuck after this. I need to find a non-linear relationship to predict how log (X Variable) will affect log (Y Variable). Would simply using this log-log model be…
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Minimum distance estimator

I'm trying to replicate the paper of Blundell et al. (2008) to separate permanent and transitory shocks on income on a panel dataset. He solves the non-linear system of equations using Chamberlain's minimum distance estimator (it is shown in the…
user4131
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Correlation and colinearity in nonlinear regression?

i have a new data set which is basically as bad as the last (same sort of data) and have been asked to try non linear regression on it, with the focus on partition (I will be using boosting and bagging). The dependent variable is continuous…
Samuel
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