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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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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470 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
2k 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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92 views

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
591 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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66 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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64 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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58 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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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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1answer
213 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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1answer
589 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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91 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 don't wanna run a GLMM just to put the blocks as a ...
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1answer
110 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
913 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
429 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
2k 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
56 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
179 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
126 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
1k 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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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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102 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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70 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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551 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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196 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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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
50 views

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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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
676 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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219 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
9k 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 ...
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1answer
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Explanation of Mincer-Zarnowiz regression

I am confused about what the Mincer-Zarnowiz regression does. What I understand is that it checks if the forecast we make is biased or not. Let's say we have the following example: ...
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1answer
108 views

Both variables of my GLMM output are significant. Don't know how to interpret it?

This is more of an interpretation question than anything. I have run a GLMM with two fixed factors (both of which have two levels) and two random factors. The outputs from the model are as such: <...
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804 views

No intercept model with multiple categorical variables - linear regression

Does running a no-intercept model with multiple categorical predictors and interaction between the predictors result in valid estimates? I am modeling differences within paired data and am using a no-...
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Why does the intercept account for the measurement error in the predictor of a simple regression model?

Baguley (2012) mentions that regression, compared to correlation, is usually deemed the superior statistical technique. Among some of the reasons mentioned, he states that in regression, X (predictor) ...
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1answer
1k views

Specifying constant as intercept in logistic regression using R

I am trying to replicate a logistic regression analysis from a paper using R in lme4 (the specific analysis in the paper uses the glmfit function in Matlab). In it, ...
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3answers
635 views

In a regression is the Y-intercept a measure of unaccounted biases?

I have been working on a set of data which contains information on the width, age, weight of statues and relate them to the price (I am not actually working on that, but I cannot disclose the topic of ...
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2answers
4k views

Bias initialization in convolutional neural network

What is the correct way to initialize biases in convolutional neural networks (tf.zeros, tf.truncated_normal, ...
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2k views

Explain the fit_intercept parameter in some scikit learn classifiers [duplicate]

I'm fairly new to machine learning and I am using the Linear SVM classifier to classify some text data and I was wondering what exactly does the fit_intercept parameter does and what would be a good ...