Questions tagged [nonlinear]

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Linear Or Non-Linear Relationship?

I am confused as to whether relationship between height (y) and weight (x) in the graph below is linear? As my assumption is if we fit a regression line, it wont be a good fit as one x value has ...
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4 views

Ideal copula family to evaluate a joint CDF of a process with non-linear dependency?

Say a process exhibits ARCH/GARCH type non-linear dependence and we wish to evaluate its joint CDF. Without relying on a criterion, such as AIC what is the best copula family that fits this framework? ...
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30 views

Statistical Testing of Non-linear Model Parameters

I have produced three non-linear 4-parameter logistic curves based on some experimental observations using three different measurement devices. Each curve shows the measurement of density decline ...
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15 views

Modeling data coming from different sensors

Let us say that we measure a continuous phenomenon Y with multiple sensors. Despite the calibration process, we expect that the responses of the sensors are not exactly the sames. Some will have a ...
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Transformation to linear regression. Help!

There is one problem where a regression is like this 𝑦𝑖 = (𝛼 + 𝛽𝑥𝑖)*𝜀. How could I get the OLS estimator? Maybe trying a transformation? I just trying by taking log, but still no result. Also, ...
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How do I evaluate correlation, that appears non-linear

Directed here from StackOverflow Let's say I want to assess if there is a correlation between two fields, one of which I know to have a power distribution. A lot of the information I read assumes ...
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9 views

L-BFGS-B. Forces early stop with no 0 gradient

I am minimizing a non-linear function which is close to linear with L-BFGS-B with scipy.optimize. The issue is that I have a non zero jacobian, low levels of tolerance but the algorithm keeps early ...
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1answer
20 views

Granger causality test - What dependencies are being captured?

I'm currently reading on the Granger causality test but different sources seem to be contradicting. In the original paper Using the mutual information coefficient to identify lags in nonlinear models ...
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11 views

Libraries for non-linear PCA visualization

Are there any open-source python libraries or repositories that can be used to create nonlinear biplots? Or, more generally, are there open-source python libraries to visualize non-linear PCA or VAE ...
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26 views

Q, method for non-linear mixed effect model using nlme?

I'm trying to apply non-linear mixed effect model in my data, but it does not work at all. My code is, ...
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1answer
66 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 ...
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18 views

Nonlinearity of Neural Networks [duplicate]

Most books and articles often refer to Neural Networks as capturing nonlinear relationships between the dependent and independent variables, as well as allowing for interactions between the ...
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2answers
36 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 ...
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1answer
33 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",...
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Will using an interaction dummy give the same estimate as stratifying by that category for non-linear regressions?

I know that with linear; $Y = A_1 + A_2D + B_1X + B_2X*D$ that $A_1 + A_2 = C_1$ and $B_1 + B_2 = E_1$ where $Y = C_1 + E_1X$ | stratified over $D = 1$ But I can't seem to replicate my results ...
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26 views

Binary Non Linear Regression with Time Series and Group Interaction Effect

First post so I'll try to be as specific as possible. My design is as follows: 2 groups: Control and Treatment 5 min test of movement within an arena with a zone of interest Binary Dependent ...
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26 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 ...
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42 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, ...
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25 views

Machine learning methods for panel data

I have a panel data in which I have time series value for a particular stock with multiple features. Similarly, I have such datasets for multiple stocks, the features are consistent across stocks(...
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1answer
32 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 ...
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2answers
128 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 ...
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11 views

Specifying interactions in nonlinear growth curve models

I have a nonlinear growth curve model with Time and Time^2 as well as one time-varying predictor (level 2) and one time-invariant variable (level1). I want to test interaction effects. Normally I ...
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14 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 ...
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10 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 ...
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11 views

Testing cubic moderation of linear effects

I’m trying to test cubic moderation of linear effects and plot Johnson-Neyman regions of significance (or something similar that would tell me the time cubic values at which the effect becomes ...
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44 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 ...
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117 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'. ...
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1answer
63 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 ...
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54 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 ...
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25 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 ...
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1answer
42 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 ...
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25 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, ...
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1answer
112 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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24 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 ...
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26 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 ...
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1answer
52 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 ...
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17 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 ...
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18 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 ...
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74 views

How to do the RESET test on an AR model?

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1answer
36 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 ...
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1answer
99 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 ...
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44 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: ...
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271 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 ...
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1answer
42 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 ...
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136 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 ...
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2answers
51 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 ...
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1answer
89 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 ...
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1answer
129 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 ...
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1answer
331 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, ...
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80 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. ...

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