Questions tagged [nonlinear]
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352
questions
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Nonlinearity of model using Sobol indices
I'm analyzing a computationally demanding numeric model where I want to show that nonlinearities play a certain role for my problem. I want to do this using Sobol sensitivity indices of first oder by ...
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1
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84
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How to estimate this specific logistic regression model which is not linear in its parameters?
A. Suppose I want to fit the regression
$Y = f(\lambda X_1 + (1-\lambda) X_2)$
where $f(x) = ax^2 + bx + c$, and $\lambda$, a, b, c are to be estimated using the data.
This is nonlinear, but it's ...
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0
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58
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crossed random effects in nonlinear mixed-effects model
I am a beginner in mixed effects modeling and am trying to find some useful code to solve my current problem. Specifically, I'm having some problems with model fitting. I'm looking for a ...
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1
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31
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Interpertation of a conditional quadratic latent growth curve model (i.e., with predictors)
I have a conditional quadratic latent growth curve model and am wondering how to interpret the results.
My predictor of interest is significantly associated with the slope factor (B = -0.45, p = .001) ...
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123
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How to calculate covariance matrix in nonlinear least squares
I am fitting a nonlinear model to observations by using least squares to estimated the model parameters.
Theoretically, the covariance matrix of the parameters can be estimated by inverting the ...
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Specifying continuous autoregressive covariance structure in multilevel daily diary model
I have a daily diary dataset with daily ratings of mood (e.g., daily rating of happiness) between two treatment conditions. The complete number of days of ratings vary widely across participants and ...
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30
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How to deal with a few number of cluster (n<15) for nonlinear?
I am currently trying to address a few number of clusters (n<15) for a nonlinear model (multinomial logit).
I have already gotten an idea from Cameron et al. (2008) for a linear model to use "...
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56
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Can All Regression Supervised Machine Learning Models Be Viewed as Linear Models Over Transformed Features?
I've been studying various supervised machine learning algorithms for regression tasks, and I've come across an interesting perspective suggesting all machine learning models could be represented as ...
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Prove identifiability of a nonlinear model with Markov Process
I have the following statistical model where for $w \in (1,2,...,W)$, $\theta = (\eta, \mu, \sigma^2)$, and for fixed $\beta$
$$Y_w = f(\theta, \beta, w) + \gamma_w$$
where
$$\gamma_w \sim N(\gamma_{w+...
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Regression model : does non-linearity imply interaction effect?
I would like to know more on the relation between non linearity and interaction effect. For example, if we have a linear model of the form
$$
y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \epsilon
$$
we ...
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Extended Kalman Filter for estimating angle using tan measurement function and two measurements
I'm attempting to implement an extended Kalman filter (EKF) to estimate an angle $\alpha$ given measurements of two scalars $x$ and $y$ where the measurement function is $\alpha=atan(\frac{y}{x})$. ...
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88
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Multiplicative linear model
I am considering the model:
$$
y_t = \beta_0\left(\Pi_{i=0}^{K}x_{i,t}^{\beta_i}\right)\left(\Pi_{j = K+1}^{L}e^{\beta_{j}x_{j,t}}\right)
$$
where we want to have multiplicative effect between ...
- 111
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8
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Lagged nonlinear independent variable?
I came across a paper that write the following:
The first set of independent variables, REPRESSION(1)i,t-1, REPRESSION(2)i,t-1, REPRESSION(3)i,t-1, REPRESSION(4)i,t-1, are binary indicators measuring ...
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1
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122
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Can nonlinear regression identify this equation?
I want to estimate the following regression equation:
$y = a + \frac{b}{r*x + 1}$
x is the independent variable, and a, b and r are parameters to be estimated. I have been told that the model is not ...
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0
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28
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What would be a good machine learning model to predict how independent variables with low correlation affect the dependent variable?
I am currently trying to build a machine learning model to predict how a variable "age" affect the efficacy of a worker. The dataset includes many dependent variables, but the only variable ...
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Are polynomial models unreliable at data extremes? [duplicate]
I have fitted a polynomial regression (4 degree model) to describe a non-linear relationship between my two variables. My question is why does this model begin to decrease towards the right hand side ...
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how do we capture effect of X1 on other variables when its effect depends on level of X2?
imagine we have five variable X1, X2, X3, X4, X5. what I am looking to find is the effect of X1 on X3,X4,X5 when the X2 is at its lowest and highest periods.
for this, I applied the TVAR function in ...
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320
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Why do you take the natural logarithm plus one? [duplicate]
I have read in many different studies now that take the natural logarithm of one plus x.
For example, in econometrics many studies use the natural logarithm of one plus the total assets.
I do not ...
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1
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1
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88
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Non-Normal Residuals in Real World Data
I have a dataset that includes real world data (not experimental or survey data) for a set of countries year by year for 40 years. The data was collected by entities such as the World Bank and United ...
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What would be a good model fit for a rise-and-fall time series data?
I have two time series measurement of protein "activation" under two different conditions, (A) and (B). My end goal is to fit a model and use the model parameter that best describes the rate ...
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1
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370
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Interpretation of multilevel negative binomial output
I am wondering how to interpret the coefficients returned in a multilevel (repeated measures nested within person; random intercepts-only) negative binomial regression. Output is pasted below ...
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2
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1
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86
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Linear regression expression of a non-linear model
$Y=\frac{x_1x_2}{β_0+β_1x_1+β_2x_2}$
It was written on some slide of my econometrics class that such a model could be expressed in the form of a linear model, but I am struggling to derive it by ...
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453
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Are ARCH and GARCH linear or non-linear models?
Are these models considered linear models?
I was reading an article that stated that GARCH(1,1) is superior to non-linear GARCH Models.
Source: https://www.researchgate.net/publication/...
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225
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What is the definition of a non-linear estimator? I heard that ratio of estimators is non-linear
Why don't we consider nonlinear estimators for the parameters of linear regression models?
says that LASSO is a non-linear estimator.
I think LASSO has a solution via matrix multiplication. I don'...
user318514
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1
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69
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Power calculation by simulation - what do I do with model failures?
I'm trying to run a power calculation by simulation on a set of exponential decay datasets using the nlme package in R. Here's the process:
Simulate a bunch of exponentials, using some conservative ...
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1
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97
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Transformation of periodic data prior to PCA?
Basically I have periodic data (angles from -180 to 180) that I want perform a PCA on. However, since the data is periodic, a change in angle from say 170 to 10 will not be accurately reflected. I was ...
3
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1
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68
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Can Correlation based feature selection discard features that show no correlation by themselves but are meaningful only if combined?
Assuming a feature selection process based on correlation or some other metric, is it possible to overlook input features that by themselves show no actual correlation with the target values, but that ...
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Mapping Parametric Curves with auxiliary variables
The image below displays an approach of using an auxiliary variable to map the parametric curves of a standard normal pdf and cdf.
In Equation (1), z as r.v. is clearly one-dimensional. However, after ...
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549
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Using curve_fit for Non-Linear, Multi-Variate Models [Python] [closed]
Warning: ML Noob.
I have a 3D dataset (data at the bottom) with 2 feature variables and 1 target variable. Polynomial Regression produced unsatisfactory results and it seems that the relationship of ...
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0
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38
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How to test a product of a OLS estimators?
I estimated a vector $\beta $ using OLS $\hat \beta =(\hat e_1 \hat e_2 \hat e_3)$ and I have the covariance matrice $\hat v(\hat \beta )$.
How can I test this null hypothesis $H_0 : \hat e_1 \hat ...
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406
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Is Ordinal logistic regression linear or nonlinear?
Quick question, is ordinal logistic regression a linear or nonlinear model?
Finding different sources supporting the other, and the more I read the more I get confused myself.
Perse, it should fall ...
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Advice on fitting curve to three-pooled plant decomposition model in r
I have just finished running a plant decomposition experiment measuring the decomposition of pine needles across climate and lithological types. We have mass loss, plant chemistry data (c, n, labile ...
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Need a predictive (binary outcome) model for a set of binary variables and one continuous variable
I have a data set of about 1600 binary results, that I want to predict from 9 binary variables and a continuous variable. The relationship between the continuous variable and the result variable by ...
0
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1
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115
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Fitting a cubic-like curve to data in R
I tried using nls() in R to fit the following expression to a set of data:
where g=9.8, alpha & B_0 are unknown, a = 0.01, z_0 = 0.3 such that:
theory <- as.formula(V~-(9.8)ab*(pi)(0.02^2)(T)(...
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Distribution of product of samples from two Normal distributions [duplicate]
Hello!
I have two normally distributed random variables $M \sim N(\mu_1,\sigma_1^2)$ and $V \sim N(\mu_2,\sigma_2^2)$ having physical meaning as $M$ - mass and $V$ - volume.
I need to figure out the ...
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0
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54
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Additive error model for non-linear case
I have checked other questions regarding additive noise model, but I could not convince myself for non-linear case. Assume the data vector $\mathbf{d}$ is described by a possibly non-linear ...
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1
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73
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Kaplan's Non-Linearity Test
I've been searching for an R package or function that applies the Kaplan non-linearity test to univariate time series but they are nowhere to be found. Such test has been widely applied in the ...
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639
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Possible non-linearity pspline Cox model
Our working group ran a Cox regression with a p-spline to model the possible non-linearity of continuous variables. However, I'm a bit confused with the interpretation of the linearity or non-...
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0
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884
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How to fit logistic regression to circular data?
I've made a script that can do normal logistic regression with sigmoid(linear model). However, I have data that has a circular decision boundary and looks like this.
My question is how I can modify ...
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142
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Degrees of freedom for a $\chi^2$ with non-linear polynomial model
I have a $\chi^2$ below for some model function $F$: $$ \chi^2 = \sum_{i=1}^{i=M} \frac{\left(y_{i}-F\left(x_i;\vec{a}\right)\right)^2}{\left(\Delta y_{i}\right)^2} $$ I know that non-linear model ...
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If X^2 is not significant but X is significant, do I have to remove X^2 and run again the regression analysis?
Model DV ~ W+PDSR+Corr+(FAGDP1+FAGDP2)+log(PCGDP)+Exp+Pop+Health
FAGDP2=FAGDP1^2
Result:
After removing FAGDP2(FAGDP1^2) from the model, FAGDP1 turns to be insignificant
Am I right in removing FAGDP^...
13
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2
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RMSE vs MSE loss function - the optimization solutions are equivalent?
If we optimize a function $f$ with respect to loss $L$, which is defined as RMSE; Are we going to get the same solution as optimizing MSE ? Even, if the function $f$ is non-linear (e.g. a neural ...
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567
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Quantile regression with an exponential function
The following equation: y = a*x**b where y is a nonlinear function of x. By taking logs, the equation can be expressed as: ln(y) = ln(a) + bln(x). I would like to run a quantile regression instead of ...
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249
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standar error of non-linear regression
I'm trying to compute the standar error of a non-linear regression fit, I find the answer in this post
Non-linear regression confidence interval
But i did't find that formula in any other place,and I ...
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16
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"Nonlinear" random spatial field: an example
I want to generate a "nonlinear" random spatial field in the sense that the autocorrelation function in function of the lag/distance $h$, $\rho(h)$, should be not equal to the $R(h)$ ...
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2
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555
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Isn't ReLU just a linear function? [duplicate]
I am doing Andew Ng's Deep Learning course and he says that ReLU is better than Sigmoid, but it makes no sense to me at all.
The biggest advantage of activation functions are too get a non-linear ...
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2
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129
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Proof of how to calculate the coefficient of variation of a nonlinear function
I'm struggling to find the proof of Eq. D.14b shown in the figure below:
The variable $b$ represents the “Least Squares” best-fit to the slope between $r_e$ and $r_t$ which both depend on $X_1$ to $...
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98
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Why do we use Relu if it's mostly linear
We use activation functions in neural nets to introduce some non-linearity. Now I understand that Relu is a non-linear function and I had no problems with it.
But today I learned that when the output ...
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20
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Simultaneous interaction model with nonlinear equations
I observe many groups of 3 individuals, and I want to estimate an interaction model of the form:
$$\begin{array}{rl}
y_1&=f_1(x, y-1)+e_1\\
y_2&=f_2(x, y-2)+e_2\\
y_3&=f_3(x, y-3)+e_3
\end{...
3
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1
answer
211
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Non-normal data transformation - what does it imply exactly and what does my results mean?
I am missing some understanding here. I am inspecting the relationship between the heart rate variability (HRV) and errors in the Sustained Attention to Response Task. When I conduct a basic linear ...
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