# Questions tagged [nonlinear]

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205 views

### How to calculate confidence intervals of non linear sigmoidal fitting curve?

I'm not using R or any other stats framework, I'm trying to implement myself an algorithm to optimize the fitting curve and to calculate the EC50 confidence intervals. Problem I have is my lack of ...
42 views

### Optimization equivalence

Can someone help me with the step by step demonstration of the following equivalence used in SVM: $$maximize: m = \frac{1} {\|w\|} \equiv minimize: m =\frac{1} {2}\|w\|^2$$ I would be most grateful ...
140 views

### Including a quadratic effect for an ordinal variable in a regression analysis

It's common for many datasets to have ordinal versions of numerical variables, such as age groups (e.g. "Under 20", "20-30", "30-40", etc.) or time groups (e.g. "Less than 15 minutes", "15-30 minutes",...
27 views

### If the Lagrangian formulation also has constraints, what is then the simplification?

Consider the following constrained optimization problem. $$\begin{array}{ll} \text{minimize} & f(w)\\ \text{subject to} & g_{i}(w) \leq 0\\ & h_{j}(w) = 0\end{array}$$ The equivalent ...
204 views

### Can linear (Pearson) correlation overestimate the true value?

It's well known that Pearson correlation can underestimate the true value in case of non-linear relationship. But can it overestimate? For example, Pearson correlation of discontinuous distributions, ...
45 views

### Jacobian for function including cubic spline

I am trying to fit a measured spectrum with a linear combination of end-member spectra which are approximated by cubic spline functions ($f_1$ and $f_2$). I also need to incorporate terms that account ...
405 views

### Can I use *any* activation function in my Neural network as long as it is non-linear?

I am currently learning about Neural networks and am finding it hard to comprehend the reason why activation functions such as ReLU or sigmoid are favored. In general, I understand the need for the ...
16 views

### Nonlinear relationship in logistic regression [duplicate]

I have a binary dependent variable (infection + or -) and both continuous and categorical independent variables. One continuous independent variable (BMI) seems to be nonlinear in that the lowest and ...
13 views

### Options for nonparametric preference ranking models

What are some options for nonparametric ranking models with a probabilistic interpretation? I'm basically looking for a nonlinear/nonparametric version of a rank ordered logit model. I'm aware of ...
153 views

### Pairwise Contrast on relative change emmeans package

So I have it a Generalized Linear Mixed Model and am looking to do contrasts. However, in this case, the biochemically relevant contrast is not a simple difference of differences. It is the difference ...
303 views

### Need help: nested fixed effects in nlme()

I have two fixed effects in a nonlinear mixed effect model. One is nested in the other, as the case here: "Specie" is nested in 'category'. ...
165 views

### How to simulate non-linear regression model with splines?

I want to simulate a non linear regression model of the type $$y_i = 1 + x_i + bs(x_i)+ e_i,$$ $i=1,...,1000$, where $bs(x_i)$ is a b-spline. I have tried to use the ...
56 views

### Evaluation of variance components - mixed models

How can I evaluate if the variance components of a nonlinear mixed model make sense (assuming or not assuming treatments factor)? For instance, if I am assuming an unstructured variance-covariance ...
28 views

### Modeling approach to showing a parabolic effect is greater than that expected by scale boundaries

I have conducted an experiment where raters rate different nations on a DV. Each observation is a different nation. I calculated a mean and SD of the DV for each nation. The data we are working with ...
86 views

### Non-linear dimensionality reduction for detecting coordinate systems [closed]

I am trying to find a way to automatically find the appropriate coordinate system for a physical problem. For example, in the case of a simple pendulum, polar coordinates are the most appropriate ...
56 views

### Nonlinear fit in R only works with tightly restricting parameter bounds [duplicate]

I have a reproducible example here with an attempt to use nls to fit a nonlinear function: y = ax/(b+x) + c Even when I set the starting values to be a good, ...
311 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 ...
27 views

### Nonlinear data to use in multiple linear regression?

I am supposed to be running a multiple linear regressions to test my hypotheses. However, when first testing the assumptions that should be met before performing a linear regression, it turns out my ...
35 views

### non-linear tikhonov/ridge regularization?

For traditional ridge regression, the loss function is $loss\_function = ||A\mathbf{x}-\mathbf{b}||_2^2 + ||\Gamma\mathbf{x}||_2^2$ https://en.wikipedia.org/wiki/Tikhonov_regularization Is there a ...
92 views

### Can VARMA handle non-linear data?

I know that traditional ARIMA models cannot handle non-linear data but I was unable to find any place where it states whether if VARMA can handle non-linear data or only linear. Please clarify this ...
51 views

### Primal solution exists but dual does not

I am working on the follwoing nonlinear model. Min z=10(1-$\exp$(−3x) ) subject to: x $\leq$ 3 When I solve this problem on LINGO, I got the message "dual solution does not exist but primal ...
20 views

### Estimate the Beta Coefficients, and then find an algorithm

Referring to the photo, I need to report my beta coefficients as functions of observed Xi and Yi. I tried to reduce by taking the log of both sides but It seems I can't reduce this model because it is ...
103 views

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42 views

### Estimation of model with non linear dependent variable

I am trying to verify whether two variables are linked by a relation of the type: |y|=ax or y^2=ax. What could be the right statistical procedure to verify whether the above relations are correct and ...
136 views

### SVM non-linear decision function using hyperline

Suppose that we have a toy classification problem X -> y in 2D. In scikit learn, I solve this question with X = np.array([[2, 1], [3,1], [3, 0], [4, 0], [5, -1]]) y = np.array([0, 1, 1, 1, 0]) from ...
76 views

### Variance of the mean in case of a quadratic trend

Please allow me to use Python code to put my question across. Suppose we want to model a variable using either a linear or a quadratic trend: ...
516 views

### cumulative distribution function for non-normal distribution

From this article, I read that the author drew four versions of CDFs each plotted in different distributions (all four plots come from the same sample data) From these four plots, the author chooses ...
103 views

### accounting for age effects: two age groups and within-group age differences

I am analyzing data from a study with two groups of about 25 healthy participants each, one young (mean age ~25 [~18-~30] years) and one older (mean age 59 [45-75] years). The study was set up mainly ...
299 views

### Should I standardize my variable for regression before nonlinear feature transformation?

I would like to fit a non-linear model by doing nonlinear feature transformation first (e.g. exp, log) and then using linear regression (or regularized linear regression). However, I am stuck at ...
59 views

### Would machine learning techniques help if the linear and nonlinear relationships is so weak?

I have a cross sectional data set at hand contains four predictors to predict one outcome, I employed bivariate analyses to check whether the relationship between the dependent and independent ...
120 views

### Conterfactual estimation in machine learning model

There are various techniques to build counterfactual estimations of certain variables for linear models in observational studies. Some of those are based on comparing the change in the predicted ...
187 views

### How can I plot relationship between two variables with the constraint of initiating the S-shaped curve from (0,0) as depicted in the example below?

I don't want to run logistic regression or any such regression model. I have 8 to 10 pairs of data points and want to analyze the logistic growth model by fitting any function-generating S-shaped ...
769 views

### Neural network for predicting a non-linear function

I want to build a neural network to predict $f(x)=\exp(-x)$ for every $x$ in the interval $(0, 5)$. I randomly generated the training set uniformly in the given interval with 500K training examples, ...
84 views

### Can I statistically describe a single case/outlier vs. a distribution?

I have a dataset consisting of body weight and corresponding age for a bunch of healthy subjects (grey triangles below). I fit a nonlinear function to this data and graphed a 95% prediction interval. ...
643 views

### Using UMAP or other non-linear dimension reduction techniques on response variables prior to learning?

Background Suppose you have a training set where the response measurements are some $N$-dimensional vectors of related measurements - in my specific case, they happen to be cell viability scores for ...
1k views

### Which features should I choose to create polynomial features?

Sometimes we want to use some features in our original dataset to create polynomial features in order to add non-linearity to our model. The question is how to choose those features? Do we choose ...
703 views

### What is the difference betwen a time non-homogenous Markov Chain and a non-linear Markov Chain? Example

A time non-homogenous Markov Chain is one in which the transition probabilities are not constant over time. A non-linear Markov Chain is a model that is not linear in parameters and satisfies the ...
209 views

### How to test for overfitting in a TAR model in R?

I want to fit a threshold autoregressive model, and I'm using the tar package in R. For ARIMA models, I could check if a model was overfit by looking at the values of standard errors as compared to ...
715 views

### What is an appropriate transformation of an age variable when used as a predictor of athletic performance?

My question concerns using non-linear transformations on linear variables in regression, particularly where you believe the predictive weight might peak at some central value of the linear predictor. ...
26 views

### Linear Unconditional X-Y, Non-Linear Conditional X-Y

Intuitively, I can imagine that an unconditional (i.e., unadjusted for any covariates) Y~X relation can present as a linear relation, whereas a conditional Y~X|Z relation can present as a non-linear ...
169 views

### Exploratory factor analysis of a non-normally distributed data set with probable multicollinearity problems

I am trying to develop a scale measuring employee satisfaction regarding organizational support using spss. Most of my variables are positively skewed which should not be a problem in EFA as long as ...
887 views

### Fitting power model to data with zeros

I want to fit a power model to some data. The model is of the form y = ax^b. I can take one of two approaches: 1) I can take logs to linearize the model, and use linear regression to find values for ...
433 views

### Including error dependent on output in Gaussian Process Regression

I have a set of experimental data that I am trying to fit using Gaussian process regression (GPR) using Python's sklearn package. The only problem is that my data has an experimental standard ...
1k views

### R lmer, 3 time point longitudinal data, non linear, messy residual help!

I am new to mixed models so please go easy on me! I am attempting to longitudinally model a normally distributed continuous outcome with values in my dataset from -30-10. I have data collected at 1, ...
186 views

### upper confidence bound of a non-linear model seems wrong (predictNLS)

I have the following data and R-script: ...
252 views

### Tests to check a non-linear relationship?

I have a non-linear relationship between two variable (tested using a linear and square term). Are there any tests that can provide validation for the non-linear relationship? I have tested Lind-...
177 views

### Relevance of residual normally distributed residuals in nonlinear regression

I have a mathematical equation, based on physics, that requires estimating several parameters via nonlinear regression. I have conducted such nonlinear regression estimation with a dataset of 1100 ...
496 views

### Price Elasticity Estimation with a non-linear price schedule

How do I estimate price elasticity in a non-linear price setting? Non-linear prices are seen in utilities (electricity, water etc.) where the price per unit is determined by quantity purchased. So a ...