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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What's the difference between drift, intercept, and mean? [duplicate]

In R, stats::arima has a parameter named include.mean, and its result can contain a component named "intercept". For example, <...
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Comparing fixed intercepts of different mixed models R

Given 3 variables: y is continuous, x is continuous, z is a repeated measures factor, nested within subjects. I have two models from different data sets a and b: fitm1 <- lme(y ~ x + z, random = ~...
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glmm (poisson or negative binomial) which explain the significance of each single level [closed]

I'm using the function glmer.nb of the library MASS to analyse the effects of two fixed factors (temperature: 2 levels and salinity:3 levels) and nested random factor (Individual ID/room) on parasite ...
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Why shifted predictor value would not change OLS estimator except intercept term?

This question comes from MånsT's answer of question The least squares estimators of $β_1$,$β_2$,… are not affected by shifting. The reason is that these are the slopes of the fitting surface - ...
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716 views

Does dummy code a variable affect the intercept in a linear regression model

My colleague and I were both using R to fit a linear regression with the same dataset and same variables. The outcome variable is test grade while the independent variables are gender, age, and times ...
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Why is the intercept typed in as a 1 in stats packages (R, python)

When using statistics software, When defining your linear models, why is the intercept typed in as a 1, rather than "const" or "intercept" or something. What significance does 1 have? Is there some ...
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1answer
63 views

Fitting model without the intercept [closed]

Suppose I collected data of crop yield at a location for mutliple years and constrcut a model of the form lm(yield ~ drought_index + solar_radiation + heat_stress) ...
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410 views

How important is a statistically significant intercept?

I've created the following model: log(consumption) = a + b*log(GDP) + c*log(GDP(-1)) + d*log(consumption(-1)) The slope coefficients are all statistically ...
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611 views

Re-calibrating Intercept on logistic regression models for unbalance data

I have data-set that I’m modelling using logistic regression as land.cover~H1+H2+H3+H4+H6+H8+H14. My response and categorical variables are binary. However the number of 0 and 1 in my response ...
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1answer
441 views

OLS estimation of intercept in AR($p$) in R

I investigate the performance of the OLS estimator of an AR($3$) model given by $$ X_t=\mu+\phi_1X_{t-1}+\phi_2X_{t-2}+\phi_3X_{t-3}+\varepsilon_t $$ for $t\in\mathbb Z$ using the following code: <...
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plot between two predictors X1 and X2: [closed]

Given the following scatter plot between two predictors $X_1$ and $X_2$: Is there a way to get the number of parameters of a linear model like that? model ...
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Is it valid to solve an equation for multiple coefficients, then average them to obtain overall effect?

I have a regression model, the setup for which is as follows: I am using manyglm, a multivariate general linear model approach to determine the difference in several invertebrate species between two ...
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132 views

Interpreting intercept in multivariate linear regression when excluding some factors

This question may have already been asked, but I cannot find anything quite like what I am asking. Background and model I am using manyglm with a negative binomial distribution (from the package ...
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How should I interpret a non significant intercept in a GARCH model? [duplicate]

I am currently building a model based on a GARCH process. You can find a quick description of how the variance is modelled below. $\sigma_t^2 = \alpha_0 + \sum\limits_{i=1}^{n} \alpha_i \epsilon_{t-...
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645 views

Combining Results of Simulation Replications (Random-Intercept Logit Models under Confounding)

I've written some simulation code in R to learn about the behavior of a random-intercepts logit model under varying degrees of confounding. The simulated scenario is three points in time, two groups, ...
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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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662 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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Machine learning - use of intercept in regression? [closed]

what is the purpose of adding the intercept in regression. why we are adding the bias. How we can predict if we have only dependent variable not any independent variable.
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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
3k 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
722 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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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
79 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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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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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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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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271 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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923 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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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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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 don't wanna run a GLMM just to put the blocks as a ...
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1answer
117 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
1k 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
492 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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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
60 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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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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1answer
290 views

intercept in manually weighed regression

Why does manually weighting a regression require the intercept term to be dropped? Consider a model $$y=b_0 + b_1x + \epsilon, $$ a simple linear regression. In classically weighted regression ...
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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
163 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
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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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1answer
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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
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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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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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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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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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214 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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