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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154 views

Truncated singular value decomposition

Is it possible to get a "truncated SVD"-regularized solution for L1 norm min errors problem? $$min\|Ax-b\|_{1}$$ In L2 universe results are derived easily analytically. I want to formulate a problem ...
2
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0answers
787 views

Question about prediction bands for non-linear regression computation?

I am interested in computing prediction bands for a non-linear regression (log-logistic function with 3 parameters). I have read the Prism help page: The calculation of the confidence and ...
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3answers
315 views

Regression methods

What is the fundamental difference between: Linear regression Non linear regression Parametric regression, and Non-parametric regression? When should we use each type? How do we know what ...
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1answer
1k views

Standard error of the residuals for a non-linear model

Hi I am new to R and statistics and used to linear models. Can you please explain the output? I used it to make a growth curve. ...
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2answers
33k views

When fitting a curve, how do I calculate the 95% confidence interval for my fitted parameters?

I am fitting curves to my data to extract one parameter. However, I am unsure what the certainty of that parameter is and how I would calculate / express its $95$% confidence interval. Say for a ...
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4answers
16k views

Distinction between linear and nonlinear model

I have read some explanations about the properties of linear vs nonlinear models, but still I am sometimes not sure if a model on hand is a linear or a nonlinear one. For example, is the following ...
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2answers
4k views

Is least squares the standard method to fit a 3 parameters Gaussian function to some x and y data?

A participant in one experiment needs to decide whether a flash and a sound are simultaneous or not for many possible asynchronies between the flash and the sound (x in seconds). For each asynchrony, ...
5
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3answers
4k views

Linear regression best polynomial (or better approach to use)?

Any ideas on other polynomials I could successfully use for applying regression? My goal is a solution that has fit error strictly based on the noise. Is this possible since it is a bell-like curve? ...
4
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0answers
366 views

On nonlinear regression, fits, and transformations

I am trying to fit a nonlinear regression model in R using nls(). I have a form of the equation I want to fit to: $$y = (a \times x_{1}^c +b \times x_{2}^d) (x_{3}^...
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0answers
196 views

What is the qualitative difference between a Michaelis-Menten model and a log-linear model?

In a book chapter I am reading1 the authors compare the fit of the relationship between biodiversity and ecosystem function using both a log-linear model and a Michaelis-Menten model. The authors ...
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0answers
1k views

Compare two regression models with same degrees of freedom

I have fit a non-linear model with 3 parameters to a data set. I have a preconceived notion that one of the parameters will be one of 2 values. So I would like to compare 2 fits of the same model ...
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3answers
16k views

statistical test to see if relationship is linear or non-linear

I have an example data set as follows: ...
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2answers
1k views

Regression with correlated explanatory variables

I have variables of the following kind (coded in R): ...
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0answers
2k views

Comparing nonlinear regression coefficients from independent datasets

I performed enzyme kinetics experiments on a three independent preparations of an enzyme and produced the following three datasets which I separately fit to the Michaelis-Menten equation: $$ V= \frac{...
14
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1answer
11k views

Non-linear mixed effects regression in R

Surprisingly, I was unable to find an answer to the following question using Google: I have some biological data from several individuals that show a roughly sigmoid growth behaviour in time. Thus, I ...
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1answer
2k views

Interpretation of weights in non-linear least squares regression

I am conducting a non-linear least squares regression fit using the python scipy.optimize.curve_fit function, and am trying to better understand the weights that go into this method. I have a ...
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1answer
2k views

Why does the scaling exponent of a power law fit change so radically when the data is scaled by a constant?

Consider the following data and the code ...
5
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1answer
92 views

Different powers of coefficient - solvable within GLM?

I have model where coefficient is of different powers: $$\mbox{log} ( \mu_{i} ) = \alpha + \beta x_1 + \beta^2x_2 + \beta^3x_3 + ... + \beta^nx_n \\ \\ N_{i} \sim \mbox{Poiss} ( \mu_{i} ) $$ $N_i$ ...
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5answers
3k views

Do statisticians assume one can't over-water a plant, or am I just using the wrong search terms for curvilinear regression?

Almost everything I read about linear regression and GLM boils down to this: $y = f(x,\beta)$ where $f(x,\beta)$ is a non-increasing or non-decreasing function of $x$ and $\beta$ is the parameter you ...
2
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1answer
231 views

Nonparametric/nonlinear regression

I am looking for a survey/book on some state-of-the-art non-parametric (or nonlinear regression) methods, preferably with an inclination towards sequential data. Till date I have used ...
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1answer
2k views

Solving intercept / equivalence point / crossing point of where two Weibull regressions meet

I'm looking to solve the point where 2 opposite Weibull functions meet. I'm using the drc package, with a type 2 Weibull having 2 parameters in R. I've fit both ...
3
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1answer
90 views

Interpreting Regression Results: Combined Data Points

I'm new to statistics, so I'm having some trouble interpreting some results. Let's say I was interested in creating a daily wind speed profile for the arctic during a 30 day period. I have 5 ...
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1answer
2k views

How to model multivariate time series

I have a set of $n=1000$ samples of 4 dimensions (multivariate) where each measurement obtained from GPS tracking data is taken at a time interval representing spatial coordinates $(x,y)$, velocity. ...
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0answers
501 views

Comparing sets of parameters extracted from different exponential fits to each other for significance

I take two simultaneous measurements from two different regions of a biological system, where both signals can be modelled by simple exponential rise and decay: $$ I(t)=(1-e^{-t/\tau_{rise}})(e^{-t/\...
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0answers
883 views

Nonlinear regression: heteroskedasticity and correlated residuals

I'm performing regression analysis of some data. I believe I have to use a non-linear model with the form $y = at^b + c$ where $t$ is time. A log transform won't linearize the data here because of the ...
6
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1answer
8k views

Non-linear modelling with several variables including a categorical variable [duplicate]

I am trying to model some data regarding a predator prey interaction experiment (n=26). Predation rate is my response variable and I have 4 explanatory variables: predator density (1,2,3,4 5), ...
190
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4answers
173k views

What does the hidden layer in a neural network compute?

I'm sure many people will respond with links to 'let me google that for you', so I want to say that I've tried to figure this out so please forgive my lack of understanding here, but I cannot figure ...
4
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1answer
2k views

Fraction of variance unexplained and R-squared in linear and non-linear regression

I have a non-linear model of the following form: $y = a*x^b$ I can fit it using logarithms and a linear model or directly with a non-linear model. First approach, logarithms and linear model: <...
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4answers
20k views

How to choose initial values for nonlinear least squares fit

The question above says it all. Basically my question is for a generic fitting function (could be arbitrarily complicated) which will be nonlinear in the parameters I am trying to estimate, how does ...
5
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1answer
3k views

How do I interpret the figure output from package dlnm in R?

I am performing distributed non-linear lag models in R. I got the figure result of dlnm as shown in the vignette (pdf) on page 13: The X-axis is lag, which I ...
13
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2answers
1k views

Linear vs. nonlinear regression

I have a set of values $x$ and $y$ which are theoretically related exponentially: $y = ax^b$ One way to obtain the coefficients is by applying natural logarithms in both sides and fitting a linear ...
5
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3answers
2k views

Strange outcome when performing nonlinear least squares fit to a power law

I have a data set (given below in my MATLAB code) y vs. x and my eventual goal is to fit it to a power law $y=ax^b$ to see what exponent $b$ I get. I did some non-linear least squares fitting and ...
9
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2answers
5k views

Help me fit this non-linear multiple regression that has defied all previous efforts

EDIT: Since making this post, I have followed up with an additional post here. Summary of the text below: I am working on a model and have tried linear regression, Box Cox transformations and GAM but ...
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1answer
2k views

Why the $R^2$, AIC and BIC criteria give different “best model” for models of equal complexity?

I'm modeling growth curve of several ecosystems with respect to their rainfall-productivity relationship using a simple linear regression $\text{ANPP}(t)=a+b\cdot\text{Rain}(t)$ and a modified ...
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1answer
5k views

How to compute p-value for quadratic fit of (25) discrete data points?

Preamble: I've had a couple of statistics courses @ uni, but can't really say I got "hooked" (I read NNT's Black Swan before starting the degree :), hence the depth of my statistical knowledge ...
4
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2answers
6k views

How to test a curvilinear relationship in a logistic regression

I was looking for some information about curvilinear relationships (quadratic function, to be precise) in logistic regression online, and couldn't really find much about it. I am interested if that ...
4
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1answer
984 views

Behavior of $R^2$ in non-linear models

I am a bit stumped on the behavior of $R^2$ in non-linear models. Below is some data and two hyperbolic fits. One in which two parameters are estimated (Model $m_1$), and another in which one ...
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0answers
91 views

How to code separate data for a regression parameter in nonlinear regression?

Say I have a bunch of measurements over a range of my independent variable (example data at the end) and I want to fit them to an equation such as a classic pharmacological inhibition curve: $Y=B+\...
3
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0answers
569 views

Is there an R package for nonlinear mixed effects model with spatial autocorrelation? [closed]

I want to fit a nonlinear mixed effects model for repeated measures data. The subjects on which the measures were repeated are spatially structured. Is there a package in R for this? I also have ...
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0answers
161 views

GRM or mixed effect models

In experiment I have measured the grow of one plant on 40 locations. At one location different number of plants were measured, but always the same species. The distribution of response variable is log-...
22
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2answers
6k views

Regression for a model of form $y=ax^k$?

I have a dataset which is statistics from a web discussion forum. I'm looking at the distribution of the number of replies a topic is expected to have. In particular, I've created a dataset which has ...
4
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1answer
1k views

Standard errors of regression coefficients based on sample size

For any particular nonlinear regression: $$Y_i = f(\mathbb{x_i},\theta) + \epsilon_i, i=1,...,n$$ I currently have standard errors for each of the $\theta_j$ obtained via the Gauss-Newton algorithm ...
5
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1answer
477 views

Nonlinear regression: Confidence intervals on transformed or untransformed parameters?

Suppose I am using a standard inhibition model to find biochemical parameters that fit my data. The equation is: $y = \frac{A}{{1 + \exp \left( {\ln \left[ S \right] - \ln IC_{50}} \right)}} $ where ...
4
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0answers
94 views

Can parameter uncertainties be salvaged when the residuals are correlated?

I have a nonlinear physical model for which I'm trying to determine parameter uncertainties using Monte Carlo. Instead of describing the nitty-gritty details, I will use a series of figures: The ...
0
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0answers
284 views

What method is better to model percentage response with each subject measured two times and heteroscedastic error?

The response was calculated as $\frac{Control-Observation}{Control}*100\%$. Raw values of $Control$ and $Observation$ are not available, I have only calculated values. Each value was measured twice. ...
3
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2answers
1k views

User-defined correlation matrix in R package nlme with negative values

I have a nonlinear model with residuals that are negatively autocorrelated at short distances. I can find no spatial correlation structures in nlme that can ...
2
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2answers
105 views

Sequential problem for n=1, non linear regression

I am trying to understand an example in my stats course notes, the example relates to calculating the best value for the next experiment. The function of the line is very simple: $$\ln(Y_i) = \ln(\...
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2answers
1k views

Formula for non-linear regression in R

I want to know if it is possible for a library in R to evaluate the association of independent variables and create a formula? I am trying to come up with a model to predict power consumption of a ...
3
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1answer
792 views

Fit a smooth approximation line

I have a simulated data set and I want to fit a "smooth approximation line" like the image I have provided. 1- Is it possible to do this in Excel or Matlab? May I have a pointer on how to do it? 2- ...
1
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1answer
219 views

Select outliers with standard deviation after a nonlinear regression

I've performed an non linear regression with 3 variables and 5 parameters, using Wolfram Mathematica. Now I want to detect the outliers that are far from 2*(standard deviation) of my function. I've ...