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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Non-linear least square minimization using for three-dimensional data [on hold]

I have a 3D data and I would like to fit a non-linear model to the data using lmfit. This is the code I have written but it doesn't work. ...
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15 views

Validating regression - common and best practice

Is there a reference setting out a best practice way to validate a regression (such as Lasso, but in general any automated regression), and what is done in practice? My motivation for the question is ...
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15 views

How to relate distributions?

I have 100 objects. Each object has 10 (highly correlated) attributes that I can measure. For each object, I obtain 10000 samples of that object's attributes. I now want to relate the attributes ...
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10 views

Why doesn't the logistic regression model include error? [duplicate]

I know it comes from the fact that y is a vector that only has binary values, but I'm looking for a better explanation...
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1answer
34 views

What the interpretation when both the non-squared and squared term are significant?

I have a logistic regression model and added for a curvelinear effect both the non squared term and a squared term to the regression model. They are however, both significant. How do i interpret this? ...
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2answers
36 views

Help interpreting interaction terms in proportional cumulative logistic regression- ordinal regression

I am using the polr() function in R to analyze the relationship between a students score on their first exam, their score in their prerequisite course, and their beginning of semester GPA on their ...
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28 views

Which non-parametric multiple-regression methods are computationally efficient with respect to the number of regressors?

I did some regression in R with random forests and got some decent results, $1-\sum{|e_i|}/\sum{|y_i-\bar{y}|}=0.692$, but I want to do better than this. Through my research, I have concluded that the ...
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2answers
45 views

How to interpret Quadratic Terms

I'm answering a practice exam questions, and having trouble with one on quadratic terms. Could someone give me a quick summery of 1) why they are sometimes included? 2) How to interpret them? In ...
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1answer
31 views

Non-linear function optimisation using nlminb function in R

I have been getting error messages in my attempt to estimate parameters in a non-linear function using nlminb function. The following is the code: ...
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1answer
33 views

Can nonlinear regression with least squares estimations be used for testing hypotheses with data containing dependent observations?

I counted the number of animals of a certain species in 6 fixed locations on a monthly basis for 18 months. I now would like to test the effects of location, starting density, and time on the dynamics ...
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11 views

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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33 views

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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25 views

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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8 views

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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2answers
80 views

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
35 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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9 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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4 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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18 views

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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12 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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17 views

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
19 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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13 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
28 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
40 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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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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30 views

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
61 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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16 views

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
60 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
25 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
44 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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48 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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28 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
49 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
51 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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21 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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9 views

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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16 views

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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26 views

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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25 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
33 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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15 views

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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24 views

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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23 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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4answers
146 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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22 views

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 ...