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.
1,167
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How to model suspected piecewise-linear data with a lasso GLM
My data consist ~130 observations. Each observation has several thousand features (including many collinear or otherwise useless features) and a position along a single spatial dimension. Some sets of ...
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Which model for highly skewed data
The response variable in the dataset is highly skewed with a "ceiling effect". The errors of a fitted regression model, will thus also be skewed. I tried to fit a regression but as expected ...
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How to know errorbars on accuracy to nonlinear fit: $A(1-\cos(x+\phi))$ with poisson noise?
I am trying to write some code that accurately estimates the parameters for the following function:
$$ Y = A(1-V \cos(X+\phi)) $$,
where this output data is poisson distributed.
To do this, I first ...
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Neural network as alternative to conventional nonlinear regression?
Can I use the strength of neural networks for data analysis? Suppose I want to find a fit to a noisy sine curve $1 - V \sin(w \theta+ \phi)$ and I want to find an estimate for parameters V, $w$ and $\...
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How to do sensitivity analysis in case of non linear regression model?
Suppose I have built a complicated non-linear regression model where the dependent variable is y and the independent variables are x1, x2 and x3. In that case, how can I answer the question
if I ...
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Spatial structure in the random forest residuals
I have a data.frame which includes the response and several predictor variables. The variables were raster data which I converted them into a ...
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How to deal with a summation term in a regression model?
In the following fixed-effects model, $EI$ is a dummy variable indicating an economic integration agreement in place between $i$ and $j$. $A$ is used to index the specific agreement an $i, j$ pair ...
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Relative variable importance/explained variation from a single model fit
I am seeking a measure of relative variable importance or relative explained variation that will apply to all types of linear and nonlinear regression models and that requires only fitting one model. ...
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GAM - factor smooth and main effects for both variables?
I am working with data on cuteness judgements and size judgments for differently named fantasy creatures. The interesting part ...
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DLNM: centering of continuous variables
DLNM centers the basis variables at the mean of the continuous variables. The value at which the variable is centered becomes the reference. How do I change the centered/reference value? As per the ...
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Interpreting linear and quadratic terms with same sign
I am running a second order model with betweenness centrality and closeness centrality as independent variables and cognitive demand as dependent variable.
The results shows that betweenness ...
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Adding a categorical variable to a model fit for comparing parameter estimates?
I am fitting a non-linear model to multiples species where the y is growth rate and x is irradiance. These growth-irradiance curves are common and there is a great r package 'phytotools' that ...
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Anyway to transform data with a varying derivative into something that can give me comparative percent changes everywhere?
Sorry about the confusing title, I am so confused that I don't even know how to frame the question.
I have a device that gives me two sets of output values depending on how I set the surface charge of ...
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Spliced Distributions Framework for python
There is an article Fat-Tailed Regression Modeling with Spliced
Distributions
that describes fat-tailed regression modeling by fitting the distribution consisting of N components (different ...
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Multiple Regression with Second Factor that Increases Volatility
I'm trying to estimate y, how likely a quantity is to increase/decrease by x1% using historical data. This part is pretty straightforward. I check history for how many times that quantity has ...
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Why do we seek to find a model that approximates all data instead of finding a function that fits all data?
I tried to learn the principle idea of regressions. As I understand, the aim is to find a model that represents the relation between the x numbers and the y numbers, so that we can understand the ...
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Projection pursuit regression
Projection pursuit regression (PPR) is described in Hastie et al.'s The Elements of Statistical Learning in the chapter on neural networks. The algorithm was introduced by Friedman and Stuetzle (1981)....
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Is there any way I can improve my interrupted time series analysis on this data?
I ran a simple ordinary least squares (OLS) model of the form
y = b_0 + b_1 * T + b_2 * D + b_3 * P + e
where y is the number of murders in a given month, T is the number of months passed from the ...
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How can I compare performance between 100 groups?
I want to compare performance between 100 groups. Each group can be described by a value, say group size. In other words, I want to see how performance changes with group size.
Each group has multiple ...
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Does mean of residuals become zero in least-squares fitting of nonlinear regression model?
It is well known that the (sample) mean of residuals becomes zero in an unweighted OLS fitting of a linear regression model. How about the case for the nonlinear model?
I have numerically tested ...
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Testing for conditional independence with nonlinear relationships
I am reading about the IC and IC* (Inductive Causation) algorithms for discovering DAGs from observations. The first step of the algorithm is for each pair of variables a and b, search for a set of ...
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What does 'linear' word in multiple linear regression and linearity assumption in multiple linear regression mean? [duplicate]
I am studying linear regression. I want to ask is the linear word in multiple linear regression refers to the linear relationship between the target variable and each of the regression coefficients ...
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When adding a confidence interval "manually", doesn't visually appear to cover most cases [duplicate]
I have a non linear regression model that is based on an exponential decay function. When I try to add a confidence interval, instead of using the models in built 'confidence interval' prediction ...
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Estimating the decay parameter in Exponentially Weighted Moving Average (EWMA) model
Given the data $y_t$, $t=1, \cdots ,N$; I would like to estimate the decay parameter $\lambda$ in Exponentially Weighted Moving Average (EWMA) model, such that
$y_{t+1} = \sum_{k=0}^K \lambda^k y_{t - ...
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What are the comparative advantages and disadvantages of interpreting regression output using marginal effects vs. ratios?
In models with a discrete dependent variable and/or linear models with non-linear right-hand specifications (interactions, polynomials, etc.), interpreting the association between Y and BX becomes ...
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How should I use a larger dataset with fewer variables to help create a good model of a smaller dataset with more variables?
I have two data sets, DF1 and DF2.
DF1 has millions of observations, and 20 variables.
DF2 has ~100,000 observations, and 40 variables. The DF1 variables are a subset of the DF2 variables.
I want to ...
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25
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Non-Linear data fitting for kinetic data
I am trying to fit a two_site model which I derived, (basically, rate as a function of pressures of reactants and products) to my experimental data. Just want to check if the logic below is fine, ...
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How to interpret results of a latent basis analysis when the estimated lambda exceeds 1?
I have ran a latent basis analysis and got the results below.
S BY
AE1 0.000 0.000 999.000 999.000
AE2 0.714 0.185 3.867 0.000
AE3 ...
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Singular gradient in non-linear least squares (non-identifiability question)
I'm trying to conduct a non-linear least squares via the nls function. The right-hand side (non-linear) function is as follows:
$-7 \ sigmoid(\theta_1 - x\beta) - 3 \ sigmoid(\theta_2 -x\beta) - 4 \ ...
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Difference in difference marginal probability from logistic model
I am trying to estimate the interaction term from a glmer model as a marginal probability contrast using emmeans. I can calculate the difference in differences marginal probability, but I was assuming ...
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Fitting a model with data that are truly "not applicable"
What model-fitting methods are available for data sets that have values that are truly "not applicable"?
After reading about imputation, I've realized that my data set does not have "...
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Optimizing Constants in a Function with a Square Root Term
I am working on a curve fitting problem where I have a series of real data points, and I want to fit a curve to this data. The derivative of the function I am trying to fit has the form:
f'(x) = -sqrt(...
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Non-linear model where the prediction is computationally fast
I am looking for a fast model that can fit several predictors $X$ to a non-linear response $y$.
To show examples of the non-linearity of the response, I have generated the plots below by sampling ...
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Non-linear mixed effect model versus linear mixed model with quadratic terms, which one to choose?
I am in the process of modeling the predicted immune response since time to last drug dose. Please note that this is illustrative and not really the real context. I have been using ...
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Popcorn- what's the best way to compare the fit non-linear models for data that is not very complex?
I popped 7 bags of popcorn in 30 second increments and found the percentage of popped kernels in each time frame.
I manipulated this data with sinusoidal, exponential, and cubic models. There is lots ...
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Regression model : does non-linearity imply interaction effect?
I would like to know more on the relation between non linearity and interaction effect. For example, if we have a linear model of the form
$$
y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \epsilon
$$
we ...
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How to do Multiple Comparisons of Fitted mle2 Model Coefficients
Is there a way to do a multiple comparison test (similar to tukey HSD test) of coefficient estimates from a mle2 model in R?
Here is my specific application:
I have a large dataset containing ...
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271
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Fit a non-linear model in R with restrictions
I'm trying to fit a model to some data in R. To simplify the question, I'll use an example.
If the model that describes my process is y = f(a, b) where ...
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69
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Fitting a nonlinear model for a CDF
I have two questions in general here. Suppose I am recording data in time and the response that I am collecting is a monotonic curve that goes from 0 to 1 (sort of a like a CDF). I was thinking of ...
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Statistical analysis of nonlinear equation
I have the following equation:
$C_i = \frac{EF_eS_i\delta_wW_j(\frac{t_i}{t_j})^m(\frac{v_i}{v_j})^n\alpha_w\gamma_f}{dwtD_i}$
where $S_i = S_{base}(.455L_i^2-.710L_i+1.280)$
And $L_i = \frac{v_i}{v_j}...
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Non-linear regression. Need some help implementing a model from a paper
I found this paper very useful for my research, however, I'm not familiar with non-linear regressions and I'm finding it tricky replicating it.
Using the first f=model for example:
...
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Simple logistic regression - calculate likelihood by hand
I am following Introduction to Linear Regression Analysis by Montgomery, Peck Vining and on p. 430 they present the likelihood ratio test. It says that
$$
\text{LR} = 2 \left[\ln(L(\text{FM})) - \ln(L(...
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Multiple Linear regression unmet assumptions, what can I do?
I need your help with some work I am doing.
Some context first:
I am writing a dissertation for my master. The topic is about perceived trust in Smart Home technology. I launched a survey with a ...
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Lower limit for NLME regression
I am using NLME packege in R to perform non linear regression.
The aim of the model is to estimate parameters related with gaseous weight loss from different silages.
I have defined my function as:
<...
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What statistical test should be used to test the relationship between the variables for a non-linear data set?
I am currently conducting an experiment and I am struggling to find a statistical test to test the relationship between my independent and dependent variables. My research is to find the relationship ...
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Non-linear formulas in mgcv
in brms (which is heavily based on mgcv) there is a possibility to define non-linear formulas (meaning not linear in parameters). However, for different reasons I need to use mgcv.
E.g. the model
<...
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LPM vs. logistic regression with complete separation of data points
I can estimate a linear probability model on about 126,000 firm-quarter observations, but estimating the same model using logistic regression drops the usable sample to only about 75,000 observations ...
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How can I combine model parameter uncertainty and input uncertainty?
Suppose I have a finite data sample $\mathbf{S} = \{ (\mathbf{x}^{(1)}, \mathbf{y}^{(1)}), \dots, (\mathbf{x}^{(N)}, \mathbf{y}^{(N)}) \}$ from an unknown data-generating function of the form
$$ \...
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How to compute confidence interval of function of Gaussian Process Resgression
I have some data that I have modeled as a function of two Gaussian Process Regression models $X_i(p_i)$, where $p_i$ is a parameter, so my regression models is: $y(p_1, p_2) = f(X_1, X_2) = X_1(p_1)*(...
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Building a hybrid model? From a Random Forest and a OLS linear regressions
Cureently, I am conducting a regression study of household expenditure (target variable) from a set of determiants (income, household size, ...) in Malaysia using OLS and Random Forest. It is a long ...
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