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.

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Neural Net Regression SSE Loss

$$ y_i-\bar{y} = (y_i - \hat{y_i} + \hat{y_i} - \bar{y}) = (y_i - \hat{y_i}) + (\hat{y_i} - \bar{y}) $$ $$( y_i-\bar{y})^2 = \Big[ (y_i - \hat{y_i}) + (\hat{y_i} - \bar{y}) \Big]^2 = (y_i - \hat{...
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Grouped Logit vs. Non-Linear Least Squares vs. Negative Binomial w/ Exposure?

I'm currently working on a project looking at the effect of competition on the type of appeals candidates make in their campaign advertisements. My dataset consists of a list of candidates, the ...
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36 views

Checking non linear effects in LASSO regression

This might be a weird question and I understand that LASSO is mainly using as a variable selection method. But I want to know that is it possible to check non-linear effects of a LASSO logistic ...
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1answer
29 views

Bell-curve shape regression [duplicate]

I am trying to fit some data that looks like a bell-curve: we reach a maximum at some value close to the mean, then the graph falls towards zero as we get further away from it. I am not the "owner" of ...
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26 views

Residuals in OLS/linear regression with restricted cubic splines

I have a dataset where dependent variable (y) seems to be nonlinearly associated to independent (x). Fitting a RCS in OLS seems to be a good option to assess their relationship. What assumptions ...
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27 views

Analyzing individual + aggregate-level data (with individual DV) : what statistical model to use?

Greetings, I have pooled cross-sectional survey data spanning several decades. Separately, using LexisNexis, I also created an index of issue-salience that stores the % of monthly newspaper articles ...
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8 views

Is a GARCH a Bilinear model also?

Following this quote from a 4* econometrics journal, "Note that a linear conditional mean model with ARCH disturbances can be described by a nonlinear specification without ARCH, i.e. the ...
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20 views

How to generate b-splines that are orthogonal to the corresponding variables in non-linear regression?

I want to fit a non-linear regression model of the type $$y_i = \alpha_0 + x_i\alpha_1 + s_i^T\beta + e_i,$$ $i=1,\dots,n$, $\alpha_0,\alpha_1\in{\mathbb R}$, $\beta\in {\mathbb R}^p$. I am only ...
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1answer
27 views

Can one assume two different functions that vary by group in a mixed effects model? (e.g. Group A is linear and Group B is quadratic)

I am wondering whether you can assume two different functional relationships that differ based on a group-based predictor in a mixed effects (or any) statistical model. The goal is a predictive model. ...
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1answer
28 views

Is there any statistical test to confirm if a dependent variable converges to a value as the independent variable approaches infinity?

I have a very large table with 40,000 elements, and the dependent variable appears to approach a value as the independent variable gets larger. Is there any test I can perform to confirm if the ...
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21 views

Assumptions failed in experimental design model

I'm dealing with a three-factor experimental design with two-factor interactions. The problem is model residuals does not fit any assumption (normality, homocedasticity and non-correlated residuals) ...
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1answer
90 views

Forecasting recurring orders for an online subscription business using Facebook Prophet and R

I am analyzing data from a subscription model, in which a customer must pay a recurring price at a regular interval (30 days) for access to the product. EDIT -> Direct link to daily data: https://...
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1answer
48 views

GAM factor smooth interaction--include main effect smooth?

I am working with a dataset it which I am interested in modeling an age*sex interaction in the GAMM framework. From examples I have seen and documentation I have read, this is typically accomplished ...
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2answers
111 views

How do I test a hypothesis that proposes existence of a positive relationship between two variables?

For my empirical experiment, I have analyzed the behavior between two variables. My one-sided hypothesis is "Increase variable A, then will variable B also increase." Now, I want to do a statistical ...
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11 views

Non-linear regression where dependent variables are dependent on different independent variables in R

I would like to know how to proceed with the following non linear regression analysis, which is a simplified version of my real problem. 5 Participants where asked to observe the speed of three ...
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74 views

How can I understand the complex regression models?

I can understand how it works when there are two variables in the linear regression model(the shaded circles represent the observed variables, and the white ones the latent variables): We can draw ...
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36 views

What is the best evaluation of training the sequential modeling?

It's concerned with the probabilistic modeling of the sequential dataset. As far as my understanding, well-known RNN methodologies consist of two steps: firstly, train the model representing $p(y_{i}|...
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13 views

Parameter estimations through non linear regression in R with multiple dependent and independent variables

I have the following exponential decay model: I want to estimate the following paramaters through a non linear regression: λ0, λ1, λ2 My simplfied version of my data set looks ...
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25 views

Nonlinear quantile regression SSReg analogue

I have recently remembered that $SSTot = SSRes + SSReg$ fails to hold in the case of nonlinear regression. $$ y_i-\bar{y} = (y_i - \hat{y_i} + \hat{y_i} - \bar{y}) = (y_i - \hat{y_i}) + (\hat{y_i} - ...
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15 views

How to compare two samples with not independent observations within each one?

To best of my understanding, both parametric two-sample t-test and non-parametric Mann–Whitney U test assume that observations are independent. I believe that making a permutation test (randomly ...
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2answers
74 views

Why do non-linear models like randomForest() and h2o.gbm() have the $R^2$ as one of evaluation metrics

The models I used for predicting cost are randomForest(),h20.gbm(),glmnet() and ...
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1answer
57 views

Nonlinear sin model with brms

I try to fit sin function with brms using next code: ...
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16 views

non linear mixed effect model with unbalanced data

I am using nlme to model the growth curves of individuals that are in 4 different groups, using R. The number of individuals in each group is completely unbalanced (n1=344, n2=51, n3=34, n4=25). ...
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23 views

Code incorrectly determines that a poor fit is a good fit

I'm trying to find the best polynomial fit for a set of data. It calculates the AIC for each polynomial fit of a certain degree, and then chooses the one with the lowest AIC. To my knowledge (which I ...
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1answer
25 views

Error on nonlinear regression by bootstrapping [duplicate]

There are several methods with which I am familiar for calculating the error / margins on a nonlinear regression fit. The standard method I think is the delta method used in Prism (described here): ...
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41 views

Error while curve fitting in R [closed]

I need to fit the curve y = K + B*exp{ a*(log x) + b*(log x)^2 + c*(log x)^3 }. Where a, b, c, K, B are unknown parameters. I just have 5 data points which are, <...
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27 views

Multiple Non-linear Regression with Function-based regression and Machine Learning models

I'm working on an application of Multi-nonlinear regression. Initially, I tried this algorithmically by creating a polynomial of the form A(x^p * y^q * z^r). I saw ...
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32 views

Multivariate, nonlinear regression in R

I am trying to make a chemical concentration curve, but it has been so long since I have had to use any type of math I'm having trouble getting going through iterations to find the best fit. The ...
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1answer
46 views

A non-linear regression model for within subject observations

I am trying to perform the equivalent of a repeated-measures ANOVA using data that have a non-linear relationship. There are two independent variables: Spacing between stimulus (10, 20, 35, 45, 60), ...
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1answer
24 views

Modeling two variable non-linear regression

I would like to fit a model to the data set that has two predictors, wind and relative humidity, and the response is inoculum production. The response to increasing in RH is sigmoid. I am not really ...
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17 views

Nonlinear Regression with Correlated Error

Assume I have two data sets: Experimentally measured data y for known values $x$. Assume the nature of the error in $y$ is random only and $\sigma_y$ is known/estimated. Simulated (deterministic) ...
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35 views

Question regarding statistical methodology that involves logistic regression

I used following simulated data using R to demonstrate my problem. require(lmtest) require(splines) x=rnorm(20 ,0,1) y=rep(c(0,1),times=10) Although my simulated ...
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24 views

How can I concentrate out parameters entering linearly in a partially non-linear regression?

I have model $$y_i = x_i^\top\beta + \delta \exp(w_i\eta) + \epsilon_i$$ in setting up a non-linear regression problem $$\min_{\beta,\delta,\eta} \frac{1}{2N} \sum_i^N (y_i - x_i^\top\beta - \delta \...
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1answer
38 views

When to use non-parametric regression such as kernel, generalized additive model, spline, and polynomial?

I understand that kernel regression is a form of non-linear/non-parametric regression. However, I know you can also use generalized additive models for non-linear regression, as well as polynomials ...
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60 views

Standardized MSE-style metric for nonlinear regression, chiefly neural networks

I am interested in neural network regression and if I have a model that has a level of performance that I deem acceptable. I am comfortable using MSE as a loss function, but I am not keen to use MSE ...
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0answers
32 views

Regression model form

I have the following exercise: US.pop dataset from car package contains information about USA population from 1790 to 1990. Find regression model in form of $y = a / (1 + \exp((b-x)/c) )$ for ...
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2answers
52 views

Why does the R2 value of regression improve on retraining neural network

I have two sets of data samples. Set 1 has 1900 samples and Set 2 has 1000 samples (none of which overlap with Set 1). I am using Set 1 to train my neural network and then testing it in Set 2. On ...
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37 views

Trouble fitting my data with non-linear Regression model

I have a dataset that contains tree height and diameter measurements among the tree stem. I tried to fit my data with GNLS in R, but I'm getting this "step halving factor reduced below minimum in NLS ...
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38 views

Non linear regression: $y = f(x_1) + g(x_2 - h(x_1))$

Suppose my dependent variable $y$ is generated from continuous variables $x_1$ and $x_2$ by the model, $$y = C + f(x_1) + g(x_2 - h(x_1)) + \text{noise},$$ where $f$, $g$, $h$ are smooth nice ...
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1answer
433 views

Examples of “one to many” for RNN/LSTM

Are there any examples dealing with "one to many" kind of LSTM? Basically I am trying to build a model which takes an input vector $a$ and gives an output of $[b_1; b_2 ;b_3; b_4, \ldots; b_n]$ where ...
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1answer
34 views

How to model counts of a categorical variable?

I'm interested in assessing the impact of various covariates (age, sex, Charlson comorbidity score, etc.) on the incidence rate of a pulmonary event. However, the event is not binary. Each patient ...
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21 views

Hypothesis testing for nlsList fitted coefficients

I am trying to test in R if the coefficient R10 (soil respiration at 10 °C) is significantly different between two plant types (Type1 and Type2). For this, I fitted a modified Lloyd-Taylor function ...
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1answer
47 views

How to fit a set of curves having some free and some shared parameters?

The problem I have a data set with 1 dependent and $N$ independent variables $x_1,\dots ,x_N$ (all real numbers), and need to fit a (nonlinear) function/curve $$ f_i(x_i; p_1,\dots ,p_{k_F}, r_1, \...
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como eu posso ajustar parameteros um sistema com duas equações com a função nls()? [closed]

I Ned to fit this system of equations: I'm using nls.lm(), but want to use the nls() function # rm(list= ls()) df=read.table( text =" 0 0.010000000000000 0 0....
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1answer
80 views

Hard in calculating predictor‘s Relative Importance for GAM?

Although there is no agreement upon "relative importance for predictors" with (even) linear models (one possible definition: lmg method), I would still want to know whether there are some acceptable ...
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23 views

Regression problem — which methods are appropriate?

Given: A non-differentiable, non-smooth function $f(p,q) \rightarrow R$ A set of points $S=\{(x_0,y_0), \ldots, (x_n,y_n)\}$ Bounds as $p_{min} < p < p_{max}$, and $q_{min} < q < q_{max}$...
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72 views

Multi State Models to analyze/plot disease progression and probability of being misdiagnosed

Let's say that I have the following dataset containing information for 100 patients that have been followed up for a certain number of years to check if they develop a certain disease. We know up-...
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9 views

Correct Specification for Censored Data

I have some construction data, which shows the starting year of unfinished and finished projects but don’t have any information on the completion time of finished projects. If I had data on the ...
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1answer
93 views

Residual Analysis assumptions for non-linear regression

I understand Regression analysis relies on the following assumptions about the residuals: Normally Distributed (normal plot of residuals) Be independent of each other (random and data must be time ...
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0answers
65 views

Is there a measure of “complexity” for linear/nonlinear model terms?

My apologies if this is grossly misunderstood or mis-worded, but I've been mildly bugged by a question to which I've not found a satisfactory answer. I can't say that I have seen a discussion about ...