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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Is ln(y+Δy) == β0 + β1(X+ΔX) in log-linear/non-linear regression?

I came across the following in explaining the log-linear regression model. Given the model $\log(Y_i) = β_0 + β_1X_i + u_i$ The expected value of $\log(Y)$ given $X$ is $β_0 + β_1X$. So far, so good. ...
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Best way to estimate fourier representation?

I have a time series $$x(t_n)$$ and I would like to fit the model $$A - A\cos(f t_n + \psi)$$, where the free parameters are $$A, f, \psi$$. I would expect that something with Fourier transforms could ...
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5 votes
3 answers
408 views

Testing difference between coefficients of nonlinear regression models

Let us consider following data showing sigmoidal dose-dependence for two distinct compounds (blue and red): I wonder about the best approach of comparing the blue vs red "curves" with ...
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Is there a nonlinear counterpart of multicollinearity? [closed]

Is there a nonlinear counterpart of multicolinearity. i.e. if two variables x1 and x2 are nonlinearly dependent on eachother in such a way that makes interpretation the coefficients of a specific ...
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2 votes
1 answer
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Interpreting Results of Logistic Regression when both x, y variables are nominal

I've been trying to analyze the result from my experiment. But since I'm new to the field of statistics, I'm struggling in every step, including the interpretation of results. I have 4 groups of ...
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1 answer
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Categorical independent variables for logistic regression

I'm currently struggling to find a appropriate method to analyze my experiment. Currently, I have 4 groups of subjects, and each subjects made a choice between 3 options(A or B or No choice). Below ...
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1 vote
1 answer
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Can MARS regression be used for classification?

I am dealing with a data set in which I have to classify between a diseased and a non-diseased individual. I was wondering if it is possible to adapt the MARS regression (Multivariate adaptive ...
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Test for equal parameters of two regression models: compare coefficients directly or check if interactions are zero?

I have two data sets and obtain regression models with coefficient vectors $\beta_1$ and $\beta_2$. I want to test $$H_0: \beta_1 = \beta_2$$ against the alternative that the two vectors are not equal....
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Estimating the coefficients of a non-linear regression

I am trying to estimate the coefficients $\lambda, \alpha, \beta_1, \beta_2, \gamma, \eta$ in the below equation using Python and some financial data $$ \lambda \times \text{(participation %)} \times \...
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Uniform measurement error in "errors in predictors" regression

I'm working with cancer incidence data that uses a range of ages (e.g. <1, 1-4, 5-10, ...) rather than a single value. I want to fit a model where age is a predictor. As a result, I'm curious ...
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Converting scaled parameters to unscaled parameters in exponential regression

I would like to calculate two types of bivariate exponential models on scaled data (therefore both variables are expressed as z-scores): Model 1: $$ y=b_{0}*e^{b_{1}x} + \epsilon $$ Model 2 (is ...
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Looking for the Holy Grail of nonparametric regression

Unfortunately, to state precisely the question, I need some formal preliminaries. Let $d \in \mathbb{N}$. For each $d^* \in \{1,\dots,d\}$, define $\mathcal{M}_{d^*}$ be the set of probability ...
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Derive the non-linear least squares equations for Poisson regression parameters

I have been asked to find the non-linear least squares equations for estimating the parameters of a Poisson regression, and to compare these equations to the MLE equations. More precisely: Consider ...
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Trend and Variance of Residuals for real world data

I am modeling the internal Resistance of a battery and have proposed the following equation: $$R_{int}(SOH,SOC,T,Current)=A_1+A_2*SOH+\frac{A_3*T*SOH*asinh(Current*\frac{SOC}{A_4})}{Current*SOC}+\frac{...
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Trying to predict the next ignition off for a vehicle

Overview: I have a dataset that captures 6 months of data for 1000 cars. Each car is represented by it's unique identifier. The data captures the exact timestamp when the car was turned ON and turned ...
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Estimate unknown function block using neural networks [closed]

I have a function block that outputs a single-value when fed with a signal (a measurement taken from a sensor) containing a 1000 time points. A similar case would be a function block that computes the ...
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Approximate output of unknown function using neural networks [duplicate]

I have a block that outputs a single value when fed with a time series containing a 1000 points. I also have a dataset of records of about 20000 input time series (each containing a 1000 points) and ...
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Is there an equivalent for an interaction term in linear models for non-linear regressions?

I’m working on how different temperatures affect the scaling of metabolic rate and gill area with body mass. It is commonly accepted that both metabolic rate and gill surface area increase with body ...
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Interpreting piecewise regression result

The table above, which tries to examine potential non-linearity of predictors, is from a paper about predicting in-hospital mortality in ICU patients with heart failure. As far as I understand, the ...
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How to incorporate standard error into non-linear model?

Suppose you have some function $f(x)$ which represents the mean value of an experiment related to $x$. Then $\epsilon = \sigma(x)/\sqrt{n}$ is the error associated with each point $x$. Assuming that ...
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Parameter Estimation on S1 model

I have the following model of creating a random graph on the circle: First, N nodes are uniformly distributed on the circle of radius $N/(2\pi)$ to give a node density of $1$. We sample the expected ...
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Does the number of simultaneous logins of a fixed number of users around a certain time follow a Poisson distribution?

I have an exam system, we started the exam at 9:30 am on the 21st, the number of candidates is 4,000, and the current data is the number of times candidates log in per second. There is also a ...
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1 vote
0 answers
21 views

How can I quantify this non-linear relationship where y-values peak within a narrow range of x-values?

I have plotted this data, and to me there appears to be a clear relationship between the variables (sediment accumulates when wind direction is between 150 and 250 degrees). Is there a appropriate ...
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1 answer
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Why are my random forest regression predicts valid probability distributions?

I have tabular input data where the labels correspond a probability distribution on five actions, E.g. a row might look like: x_0, x_1, ...., x_n, .1, .1, .3, .0, .5 I am using sklearn's Random forest ...
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Perfect regression results? [duplicate]

I am trying to perform multivariate logit regression on the following data: crisis on the right is the binary categorical response variable and all the other ...
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0 votes
1 answer
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what is the difference between moving average and regression

It seems both of these two approaches are appropriate to reflect the change in a data series over time. The moving average uses a local window, but the regression uses a global window. Which one is ...
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Exponential fitting in R with fixed minimal value

I need approximate datapoints by exponential function with some type of lower limit (variable "y" is price in time and I need fixed minimal value, so asymptote of exponential function cant ...
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5 votes
1 answer
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In nonlinear regression, when is MLE equivalent to least squares regression?

I recently received this one line question in a job interview and was a little stumped by it. In nonlinear regression, when is Maximum Likelihood Estimation equivalent to least squares?
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1 answer
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Regression with exponential decay

I have the data from Li et al. 2003 paper "Belowground biomass dynamics in the Carbon Budget Model of the Canadian Forest Sector". I am trying to recreate equation 6 in R so that I can ...
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Is a GMM model suitable for regression with interaction term?

For my dissertation I am looking at regressing net capital outflows against financial openness and GDP per capita like in Reinhardt, Ricci and Tressel (2013). To deal with potential endogeneity in ...
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2 answers
38 views

Combining quantile regression with binning

I'm trying to employ a framework where I uncover the marginal effects of the quantiles of one continuous variable on another continuous variable - something analogous to the Quantile-on-quantile (QQR) ...
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30 views

Regression problem with static and non-static data

I'm currently working on a project, more specifically, a regression problem. The results are not really that good, and I think it is because the features used, even though are standard features that ...
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23 views

Which Test to Run?

Please advise which statistical test (ordinal logistic regression or chi-square test) is most suitable in the following context: I want to test if the two independent variables (frequency of use of a ...
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DiD and Non-linear regression models

I am performing a simple DiD regression. My outcome variable is healthcare expenditure and I am regressing it on year, treated, the interaction term, and some controls. The treatment, in this case, is ...
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Fitting a line to absolute value of model residuals to detect heteroscedasticity

I have a series of data sets that I've fit with non-linear models (same model with different parameters for each data set). I'm trying to model the residuals e so ...
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2 votes
0 answers
27 views

Seeking a combination of nls() params that would make this fit curve slightly more acute?

I have some data with fields GrowthRate and DAY. GrowthRate. E.g. If amount is 100 on day 1 and then 110 on day2, GrowthRate is 1.1. Data look like this: ...
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Does Max break the linearity between the dependent and independent variables needed for logistic regression?

I want to use logistic regression to learn the coefficients of a function looks like that (a - the variables and w - the coefficients): y = max(a1w1 , a2w2) + max(max(a3w3 , a4w4) , max(a5b5 , a6b6)) +...
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How to clean dataset in order to fit to a curve? [duplicate]

I'm trying to fit a dataset to a curve for while, but I'm not managing. The goal is to obtain a curve with equation that fits the data so I can get the parameter x to any value of y. The blue dataset ...
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5 votes
3 answers
119 views

Controlling for non-linear variable in non-linear modeling of response

I need to model a continuous response variable $y$ based on continuous features $x_1, ..., x_n$ while controlling for another continuous feature $x_c$. The intent is to understand how much an increase ...
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1 answer
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Decay function (e.g. weibull?) with numeric (i.e. not survival analysis) data

An example data frame: ...
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1 vote
0 answers
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How can I make a prediction interval for a future response (not its mean) in regression by using bootstrap?

I'd like to know how I can use bootstrap to predict the confidence interval for a future response (not for its mean) no matter what theorical model and error distribution are, I know I can train the ...
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0 votes
0 answers
15 views

Relationship between two conditional expectation functions where one of them has a constant

I have two conditional expectation functions: E(log Y|X) = β0+β1X and E(log cY|X) = γ0+γ1X What is the relationship between β0 and γ0 and between β1 and γ1? Since there is a constant on Y, E(log cY|X) ...
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1 vote
0 answers
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Differentiable Non Linear Regressor to Be Used with CNN

Is there a differentiable non-linear regressor? I'm after a regressor which I can write in a few lines of PyTorch which is non linear and differentiable yest stronger than all simple to use activation ...
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1 vote
1 answer
39 views

Comparing proportions of plants that died (two-way analysis with interest in interaction effect)

I want to compare the proportions of plants in an experiment that had died by the end of the growth period. I am not interested in how long it took for them to die, although I suspect some people ...
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1 vote
1 answer
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Modelling non-linearity for binary independent variables in logistic regression

I have fit a logistic regression where the response variable is binary - whether an interview candidate got the position or not - and the independent variables are a combination of continuous, ...
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1 vote
0 answers
34 views

Which test to use to test for heteroscedasticity in a non linear model/fit?

I would like to test for heteroscedasticity in a non linear fit. I have a explanatory vector x and an explained variable y and ...
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0 answers
32 views

displacement of cosinor waves (circadian activity) R

I have circadian activity data. I have managed to fit cosinor waves thanks to all the help from this post Fitting sine wave with lm in R for circadian activity- frequencies? The data is % time spent ...
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60 views

Levenberg-Marquardt made scale invariant with diagonal matrix?

From the paper Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization We now describe how to choose an effective damping matrix $D^TD$. Levenberg originally ...
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4 votes
1 answer
165 views

Difference between splines from different packages (mgcv, rms etc.)

I recently came across the mgcv package and the great potentiality of GAM. One - maybe naive - question is what is the overall difference (if there is any which is significant) with the gam() function ...
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1 vote
2 answers
161 views

Is R-squared equivalent to mean squared error for non-linear regression

As far to my knowledge r-squared should not be used in non-linear regression setup. Not only might the r2 be too high, but also the interpretation as the variance explained by the model might no ...
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