Use this tag only for regression models (q.v.) in which the response is a nonlinear functions of the *parameters* (not because it's a nonlinear function of the *predictors*).

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Very general question about linear smoothers [on hold]

So the theory regarding local polynomial regression, splines, RKHSs tends to talk exclusively about 'linear smoothers'. But if we use the values of dependent variables to determine, say, bandwidths in ...
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dependent variable in shares, independent variable log transformed

I havea question. My dependent variable is in percentage (shares of renewables in total energy supply). Hence, my variable is bounded but values are not closed to the bounds. My professor told me that ...
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Nonlinear regression vs. GLMs for estimating ED50

Are binomial GLMs better than nonlinear regression for model-fitting, and predicting ED50s and other effective dose point intercepts? In toxicology it is typical to run an experiment with a ...
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Significance testing between two hyperbolic curves

I have two curves for biological data (one-site binding). These curves were both fit using the following (Michaelis-Menten) model: BRET2 = (Bmax * RFU_RLU)/(Kd + RFU_RLU) Note: (x,y) here is ...
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How to test the significance of fitting of quadratic equation? [closed]

I have got a problem that the fitted quadratic model is significant or not, how to test it?
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How to assign defined training set, val set and test set for training a Neural net in NNtoolbox?

To find an optimal number of hidden neurons and layers in my code using feedforward net, I use cross validation technique and cvpartition function to split data. Now my aim is to use this split data ...
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Compare MLR model to model $Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$?

If I have theoretical reasons to suppose the data might be fit with an unusual equation such as the following: $$Y_i = (\beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + \epsilon_i)^{\beta_3}$$ Can I use ...
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1answer
33 views

How do you do a non-linear Poisson? What even is it?

I have a count data that I am having trouble transforming to be linear. First, what are smoothing functions and how do I do it in R? Let's use the famous crab satellite example. If you plot width to ...
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8 views

How are the values of knots in MARS calculated?

I'm wondering how the MARS algorithm decides on the specific values for the knots which are included in the hinge functions. Thank you very much.
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Non-linear interaction terms in Stata [migrated]

Dear users and experts! I have a continuous dependent variable polity_diff and a continuous primary independent variable nb_eq. ...
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2 views

bilinear regression (or broken power law) and non-detections (upper limits)

I am trying to figure out what is the best way to fit a set of two-dimensional data (x and y, presumably independent) with two segments of linear models and a ``break point''? The tricky part of the ...
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6 views

what do the outputs of usl model mean?

I am trying to understand the summary of the universal scalibility law model: ...
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One-Step estimators for non-linear regression

'Disclosure': This question is also asked in the economics.stack community, under the tag of Econometrics, with same title. I'm not sure if it's too technical for that community. Let's suppose I ...
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11 views

Is there a p-value(or standard error) interpretation in a non parametric approach?

In a parametric world , we always report p-value or standard error in a parathesis below some coefficient from a regression , which is a significance testing. How about in a parametric world? I guess ...
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Regression of outcome variable with sinusoidal periodicity?

In linear regression of an outcome variable with sinusoidal periodicity (eg seasonal temperature variation), is it sufficient to adjust for this variation by adding a cosine function [1] as a ...
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1answer
17 views

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 ...
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6 views

Nonlinear permutation tests

I'd like to carry out additional tests on the estimated model parameters from a nonlinear model. The goals and methods are nicely presented in the 'predictmeans' package in R for linear models. Does ...
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1answer
27 views

Control Function (CF) Approach with Nonlinear Functions of Endogenous Variables

I am estimating a model using the control function approach (also "2SRI"). My model includes an endogenous variable $y_2$, an instrument $z_2$ and an interaction of $y_2$ with an exogenous variable ...
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1answer
35 views

Mixing exponential and linear regression with multiple predictors

This is the data set I am working on, trying to predict count (last column) : ...
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1answer
52 views

How does one prove asymptotic normality of the Non-linear least squares from First order conditions?

Our model is $Y=X(\beta_0)+u$, where $u\sim IID(0,\sigma_0^2I)$, and $X(\beta)$ is a non-linear function of the beta. When trying to minimize the $SSR(\beta)$ we get the following FOC: $\nabla ...
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Non-Linear Regression on model with time delay (dirac function)

here is the equation: $$y(t) = K_{2}\delta(t-\theta ) \Bigg(1-\frac{\tau_{1}e^{\frac{-(t-\theta)}{\tau_{1}}}-\tau_{2}e^{\frac{-(t-\theta)}{\tau_{2}}}}{\tau_{1}-\tau_{2}}\Bigg)$$ The parameters that ...
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1answer
57 views

How to make a model for the given data in sas?

I have a nonlinear model: $$r10^{\beta_0-\beta_1A-\beta_2B-\beta_4D-\beta_{2,4}BD} $$. I used sas to test different models. Here is the code: ...
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Exact Solution for a Nonlinear Least Squares Problem

For any linear least squares problem, we know that a unique solution always exists and that it can be explicitly written down in a closed form. My questions is that, is there any example of a ...
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1answer
50 views

How to use final svm regression model to predict new values of the dataset

I understand svm_predict function can be used to estimate or predict test output, but the arguments passed are like this svm_estimate = svmpredict(y, X, model); ...
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1answer
19 views

How to use a sigmoidal function in a multiple (non)linear regression

My data follows a sigmoidal function of the form $$y=asym/(1+e^{(xmid-x)/scale)})$$ I have taken the function from the SSLogis function in R. My supervisor and I think that there is a second variable ...
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2answers
42 views

Fitting nonlinear curves and getting parameters

I have the following data $(s_i, t_i)$: $s_i:$ -337.6 202.1 341 387 397.2 $t_i:$ 0.1 1.28 2.418 3.54 4.628 And also have the equation: $s_i= x - y*\exp(-t_i/z)$ How can I get those 3 ...
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44 views

Non-linear least squares standard error calculation in R

I am using implementations of the Levenberg-Marquardt algorithm for non-linear least squares regression based on MINPACK-1 utilizing either the R function nlsLM() from minpack.lm or an implementation ...
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24 views

when fitting non-linear data set to linear model

What is the residual standard deviation? Can I see whether the model I used is accurate or not by looking at this measure? In fact, I try to understand whether my data set is fitting to linear ...
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2answers
47 views

What is an intuitive explanation for the interaction of factors in a multiple regression?

How should one proceed when the interaction of predictors in a multiple linear regression is significant? I'm really after an "explain like I'm 5" type of explanation. Even better if it's supported ...
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1answer
49 views

Statstical test for the best algorithm for regression cross-validation

I benchmark three algrothims that construct regression models. To bechmark them I use cross-validation, so I obtain a matrix of errors (mean squared errors for example) with rows is number of ...
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19 views

How to use the off-diagonal terms of the covariance matrix when calculating confidence intervals?

The nonlinear fitting routine I use is MATLAB's fitnlm and it gives the covariance matrix. How can I take into account the off-diagonal values of this matrix to ...
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Setting bounds on multivariate data sets with possible multiple distribution types

Summary: I've got data sets whose distribution seems to differ based on where on the x-axis the data occurs. Using some common distribution mean and std dev calculations do not produce acceptable ...
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Assessing the residual independence assumption (nonlinear least squares regression diagnostics)

I would like to assess the assumptions underlying nonlinear regression models using statistical tests rather than graphical methods since I have thousands of fitting results. I am not certain ...
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Tips on how to improve a regression model

I'm developing a linear regression model (with nonlinear feature transforms) to fit some data. So far I've done the following things: I'm picking the parameter $\theta$ with the least (10-fold) ...
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24 views

How to estimate initial values for nonlinear least square fit for bimodal multivaraite data?

This is in reference to an earlier post How to choose initial values for nonlinear least squares fit This post helped me estimating parameters for unimodal multivariate data with x,y and z. However, ...
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1answer
29 views

GLM Residual Plot

I am currently completing quasi-binomial regression and I am using this line of R code to plot the residuals. plot(residuals(mylogit) ~ ...
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What is the standard results from density estimation?

Below comes from "Ruppert and Wand, Multivariate Locally weighted least squares regression, 1994, p.7 or p.1352 in the Journal" This is about using Kernel function. But I don't know what 'the ...
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Truncated dependent variable caused by the researcher!

I created my own index for the study on firms. I am interested in using the index as the dependent variable. According to other statisticians, firms with less than 100 observations used to create the ...
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21 views

find non linear dependencies in the model automatically with Lasso

I have a little knowledge on Lasso, from what i know its pretty good at feature selection and also finds the best sweet spot between bias and variance trade-off. If we are to come up with a regression ...
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138 views

How to interpret regression equations with logarithms, based on log difference being approximate to percentage change?

$y = 4 + 2.5\,x + u$ For an increase of 1 unit of $X$ (that is, $X$ to $X+1$), we expect an increase $2.5$ units of $Y$ (that is, $Y$ to $Y+2.5$). Is that right? What if there's a/an $\ln$? ...
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Which statistical test to apply for non-related variables

I have two variables, travel time to health facilities and density of violent crimes in a particular city, I need a test that I can use to statistically quantify if there is any relationship between ...
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37 views

How to interpret b in $y=1-x^{e^{bz}}$? in nonlinear regression?

What is the correct way to interpret b in this nonlinear equation $y=1-x^{e^{bz}}$? I've estimated the model and b is the percent change in y with a unit change in z, but I am unsure how to show ...
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158 views

How to find marginal effect of restricted cubic spline

I'm trying to figure out how to find the marginal effect of an interaction term from a restricted cubic spline in a non-linear model. The post Nonlinear effect in an interaction term is a good start ...
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28 views

Rules for choosing how much training data one needs to learn a Radial Basis Function (RBF) model?

I was trying to understand how much data I would need compared to the number of parameters (and to have good generalization) when I train a radial basis function (RBF) network on a regression task ...
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1answer
25 views

Improving parametric model for sinusoidal regression

I am trying to model the curve below. I am fitting the data points (dots) ...
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1answer
94 views

What is the most appropriate way to transform proportions when they are an independent variable?

I thought I understood this issue, but now I'm not as sure and I'd like to check with others before I proceed. I have two variables, X and ...
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Why are the marketing-mix variables measured as period to period percent changes in the generalized bass model?

In the paper Why the Bass Model Fits without Decision Variables, Bass et al. extend the Bass model of product diffusion to incorporate marketing mix variables. For example, if the forecaster ...
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53 views

Contribution of a term in a fraction

I have a value $$v=\frac{A_2+B_2+C_2}{A_1+B_1+C_1}.$$ I want to estimate the contribution of $A_2/A_1$ to $v$. I know it is not possible to mathematically derive $A_2/A_1$ out of $v$. My question ...
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48 views