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Questions tagged [intercept]

The intercept in regression-type models is the value of the Y variable when all X variables are 0.

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R Repeated measures with fixed intercept at 0

I am trying to run a repeated measures glmm with a fixed intercept at 0 for a longitudinal study calculating the spread of a parasite within different genotypes of Daphnia hosts, and testing for a gxg ...
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2answers
41 views

The correct random slope model for nested data

I'm trying to see how personalities of individuals change with time. The variables in my data are: 1. latency to emerge (response variable in continuous scale) measured for 204 individuals from 14 ...
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Can I average out a constant (intercept) in OLS regression?

I have a OLS regression in the form: $$Y_t=\alpha +\beta X_{t-1}+\varepsilon_{t}$$ Can I average out the constant during the OLS estimation/derivation and report, $$y_t=\beta X_{t-1}+\varepsilon_{...
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Random intercept in mixed model w/ post baseline measurements

I'm running a LMM analysis for a clinical trial (two treatment conditions, five visits) and I can't understand the exact role of a random intercept. The baseline score is not included in the outcome (...
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1answer
128 views

Regression: Insignificant Intercept [duplicate]

I ran a regression and the intercept is statistically insignificant (the p-value is greater than 0.05). I tried to look in some textbooks as to how to handle this scenario but I am still unsure. One ...
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Removing the intercept term for penalized logistic regression

I am working on lasso logistic regression and am trying to remove the intercept term from the penalty function. I have tried to use the mean centering theory but for logistic regression it can not be ...
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1answer
43 views

Penalize the intercept in lasso (L1) penalized logistic regression or not?

In logistic regression: $log(\frac{p(x)}{1-p(x)}) = \beta_0 + \beta_1x$, let $x' = \frac{x-\bar{x}}{\sigma_x}$, then in terms of the centered and scaled varaible $x'$ , $$ log(\frac{p(x')}{1-p(x')}) ...
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Modeling multilevel data with lme4

I want to find out if people who use learning strategies that fit a learning problem are more satisfied regarding their learning than people who use unfitting strategies; And also if there are ...
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StandardScale variables have same scale but in different ranges and interpretation of Y-intercept

I am applying a Multiple linear regression, have several variables X1,X2,X3 to test their impact on Y and all of them have the same scale (quantity) but in different ranges of values. Should I ...
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1answer
21 views

Adjusting the long-run expected value of a variable in a VAR model through the constant term

I am currently trying to fit a VAR model to, amongst other variables, inflation data and want the long run limit of inflation to be 2%, i.e. the ECB target. Say my VAR looks like this: $$ X_t = c + \...
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1answer
37 views

Constant and fixed effects in all sample versus subsamples

I have a panel regression for countries. There are two groups of countries, rich ($k=1$) and poor ($k=0$). The equation is: $$ Y_{ikt} = c_k + \lambda_{kt} + X_{it}\beta{k} + e_{ikt} $$ $\lambda_{kt}...
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51 views

Can I recover the level of a dummy in the constant?

In the following country-level panel data equation $$ Y_{it} = c + \lambda_t + X_{it}\beta + e_{it} $$ I use time dummies to capture the year-fixed effects, $\lambda_t$. Obviously, one dummy must be ...
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887 views

Linear regression with negative estimated value for intercept

Does a negative value of intercept suggest that the regression line provides poor fit to the data? why? and why not?
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1answer
30 views

Clarification on “intercept”?

I'm currently reading "Competition-Based Dynamic Pricing in Online Retailing: A Methodology Validated" by Fisher, Gallino, and Li. In the paper they mentioned that variables $\alpha_j$ and $\alpha_r$ ...
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1answer
43 views

suppress intercept in regression when having more than one categorical variable coded in dummy variables

friends: according to the following link https://stats.stackexchange.com/a/11068/196391 and what I saw in some papers, we can supress the intercept and consider ALL the dummy variables (which have ...
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60 views

When is it OK to calculate the AUC for a mixed-effects logistic regression model without the random intercept?

I fit a mixed-effects logistic regression model in R with glmer. There is one dependent variable, one dichotomous predictor variable, and one random intercept. The ...
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1answer
42 views

I computed ARMA equation from R manually but never got the same result with predict() or forecast() provided by R

I've got a little problem here. I've been doing analysis with time series data using ARMA, and it always turns out that the parameters I get from R didn't fit to my computation when I do it manually. ...
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13 views

How to fit a model that forces all points through zero while allowing for interaction effects

I'm trying to build a model to predict the percentage of a target audience reached as a function of the amount spent on several media channels (e.g. TV and radio) and the type of campaign. The fitted ...
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31 views

Coefficients in a Randomized Block Design

If, for example, I am running a GLM with Poisson distribution (it could be any distribution) and I have a Randomized Block Design (RBD) [Note: I dont wanna run a GLMM just to put the blocks as a ...
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R | SE of intercept | contr.sum DM

So, I am trying to estimate the 'global mean' over a set of 'treatments' (say), using a DM with a constrast structure specified by const.sum. So, for example, if there are 6 levels of said treatment ...
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1answer
46 views

AMOS: CFA testing invariance, but cannot name intercepts

I'm using AMOS to run a 2-factor model with 5 indicators each (10 in total). I'm assessing the invariance. So I'm assessing the invariance for sex. While the configural and metric invariance worked ...
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1answer
168 views

Which intercept R selects (binomial glm)?

I have a problem with an analysis. I'm doing a binomial glm with two categorical factors that are loc and trat. I do not understand how R deals with the intercept (what statistical explanation does ...
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1answer
50 views

Calculating variance components and ICC of a random intercept model by hand

When I really want to understand a measure or parameter, I tend to do the calculation by hand with simplified data. Today I have attempted to do the same with the ICC, but somehow keep failing. I was ...
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1answer
183 views

Interpreting significance of the intercept in a regression analysis

For my thesis, I'm conducting several linear regression models. In total I have 15 dependent variables, so in my appendix I have 15 regression tables including 4 models. Example: I'm trying to ...
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1answer
32 views

Include intercept/error term in logistic regression model specification

Short question, When specifying a logistic regression model as below, does one also include B0? In other words, does the bottom part of the equation look like: A. 1 + exp(-(B1X1 + B2X2) B. 1 + exp(...
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2answers
360 views

What is the reason for not including an intercept term in AR and ARMA models?

In econometric literature it is usually argued that in case of estimating an equation, an intercept term must be always included regardless of its statistical importance because removing the constant ...
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Plotting observed vs predicted values for all the combinations of the predictor variables in logistic regression

I have a logistic (glmer) model with a binary response variable, two binary, two continuous predictors and two random intercepts. In trying to see the fit of the model to the data, I am trying to make ...
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35 views

Is it necessary to include all levels as random intercepts in a multilevel model when they are perfectly nested?

I am running a mixed-effects model in R and I want to have random intercepts for two sampling levels, country and site. The ...
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1answer
49 views

Standard Error of the Intercept in ARIMAX model

I'm trying to estimate the standard error of the intercept in ARIMAX(1,0,2) model using R. Since the reported 'intercept' in regression output is actually some kind of mean value I applied this ...
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1answer
468 views

How to change a weight/bias with gradient

After watching 3Blue1Brown's tutorial series, and an array of others, I'm attempting to make my own neural network from scratch. So far, I'm able to calculate the gradient for each of the weights and ...
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Linear mixed model with three groups, alternative non-linear approachin R?

first thank you for your help. I'm quite new to to R, but specially in mixed models. Shortly i have three experimental settings from 31 subjects, i.e 3 repeated measurements from same subjects ( also ...
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25 views

Panel regression hypotheses

I want to test the difference in regression intercepts between three groups. For that I use this regression (including dummy variables) $Y_{it}=\alpha_{t}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{4}x_{4}+...
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1answer
306 views

Intercept increases in regression when adding explanatory variables

I am conducting an analysis, where I examine the size of the intercepts of three regression models (time-series). The models look something like this: $y_1=\alpha+\beta_1x_1+\varepsilon$ $y_2=\alpha+...
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1answer
458 views

Is it ok to remove the intercept in a linear regression model (OLS) if the results are really good? [duplicate]

So I've gone through this SE question and all the answers where the general consensus is that you should never remove the intercept of the linear regression model. The most upvoted answer says: The ...
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53 views

Permutation test on the intercept in MANLY(1997) framework?

We assume to have the following regression model: $Y=β_0+β_1X_1+β_2X_2+ϵ$ I recall here the Manly procedure (from another post here :How to do permutation test on model coefficients when including an ...
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When does it make sense, if ever, to remove the intercept from a logistic regression [duplicate]

I normally work with linear regression, but came across a need to use logistic regression. I started with glm(y ~ x1 + ..., data, family = binomial()). Almost none ...
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Logistic Regression with intercept as 0 [duplicate]

What will happen when the intercept of the Logistic regression is made to Zero.Does it have any effect on the co-efficients?
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78 views

Intercept equals 1 in PLS regression

I'm working with PLS and indexing in R (package plspm). For this, I'm replicating the study of Gaston Sanchez in R in his book http://www.gastonsanchez.com/PLS_Path_Modeling_with_R.pdf. In the page 77,...
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1answer
37 views

How to visualise a tiny neural network as a function

Say you have the simplest possible neural network with 1 input, 1 output and 1 hidden variable as depicted below. In this case, the activation function is logistic. I assume between x and y, the ...
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How to find Error of the Intercept with 2 IVs

First time user here... I am trying to build a 2IV regression model by hand and I'm using the Excel Analysis Toolpak (essentially the LINEST function) to cross check my numbers. I have ...
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277 views

Hypothesis at 5% significant for slope and intercept coefficient

"Conduct hypotheses tests at a 5% significance level on the intercept and slope coefficient to see if the intercept is significantly different from zero and the slope coefficient is significantly ...
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Mapping R ARIMA parameters to coefficient symbols [duplicate]

I'm trying to map the information R prints for an ARIMA model to the coefficients in the formulas that I'm familiar with. Here's what I have so far ar1 = $\varphi_1$, ar2 = $\varphi_2$, ... intercept ...
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91 views

Are HAC robust standard errors robust against autoregressive conditional heteroskedasticity?

Suppose I have a GARCH(p,q) model with constant conditional mean, \begin{aligned} y_t &= \mu + u_t, \\ u_t &= \sigma_t \varepsilon_t, \\ \sigma_t^2 &= \omega + \alpha_1 u_{t-1}^2 + \dotsc +...
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69 views

Multilevel Model, ICC = 0 which regression then?

First, I would like to present my data to discuss the following matter. I got my data from a questionanire, where I had group1 30 individuals vs group2 30 individuals. They answered on the same 6 ...
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34 views

Dropping the intercept [duplicate]

any help is appreciated. When is it OK to drop the intercept term in a Binomial GLM? That sounds like the data would have to go through the origin but that doesn't seem so bad, does it since we are ...
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1answer
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Selecting predictor in regression: What is more important - significance of the intercept or residual standard error

I am trying to find the best predictor for Leaf Area Index (LAI, a plant growth indicator) among several spectral indices (these are calculated from reflectances measured in different spectral wave ...
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1answer
439 views

Baseline adjustment in growth models: Random Intercept or Baseline Covariate

Let's say I have outcome data at four time-points (baseline, 3 months, 6 months, 12 months) which I want to regress on an explicit time variable ($t_1 = 0$, $t_2 = 1$, $t_3 = 2$, $t_4 = 3$) to ...
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1answer
48 views

How centering can ease interpretation of the intercept of a linear model

In Statistical Rethinking, Chap. 4 - page 99, when talking about table of estimates of a linear model $\mu_i = \alpha + \beta x_i$ where the objective is to estimate the height given the weigth ($x_i$)...
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90 views

Bayesian linear regression with parameter restrictions

I am a little confused on incorporating parameter restrictions in the Bayesian linear regression setup. Assume the multivariate regression $$R = \iota\alpha+X\beta+U_R$$ where $R$ is a $T \times N$ ...
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2answers
2k views

Interpreting a negative intercept in linear regression

This is my first time of having a negative intercept, so I'm a bit confused. My line of regression is: $$ \text{starting monthly income} = -7.5 + 0.75\times \text{years of education}. $$ How would ...