Questions tagged [fixed-effects-model]

In biostatistics, fixed-effects may mean population-average effects. In econometrics, fixed-effects may represent the observed quantities in terms of explanatory variables that are treated as if the quantities were non-random.

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315
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9answers
582k views

What is the difference between fixed effect, random effect and mixed effect models?

In simple terms, how would you explain (perhaps with simple examples) the difference between fixed effect, random effect and mixed effect models?
176
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3answers
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R's lmer cheat sheet

There's a lot of discussion going on on this forum about the proper way to specify various hierarchical models using lmer. I thought it would be great to have all ...
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2answers
44k views

What is a difference between random effects-, fixed effects- and marginal model?

I am trying to expand my knowledge of statistics. I come from a physical sciences background with a "recipe based" approach to statistical testing, where we say is it continuous, is it normally ...
34
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4answers
45k views

Standard error clustering in R (either manually or in plm)

I am trying to understand standard error "clustering" and how to execute in R (it is trivial in Stata). In R I have been unsuccessful using either plm or writing my ...
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6answers
5k views

What is the mathematical difference between random- and fixed-effects?

I have found a lot on the internet regarding the interpretation of random- and fixed-effects. However I could not get a source pinning down the following: What is the mathematical difference between ...
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5answers
3k views

What is the upside of treating a factor as random in a mixed model?

I have a problem embracing the benefits of labeling a model factor as random for a few reasons. To me it appears like in almost all cases the optimal solution is to treat all of the factors as fixed. ...
23
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3answers
43k views

When to use fixed effects vs using cluster SEs?

Suppose you have a single cross-section of data where individuals are located within groups (e.g. students within schools) and you wish to estimate a model of the form ...
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2answers
34k views

REML or ML to compare two mixed effects models with differing fixed effects, but with the same random effect?

Background: Note: My dataset and r-code are included below text I wish to use AIC to compare two mixed effects models generated using the lme4 package in R. Each model has one fixed effect and one ...
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2answers
3k views

Big disagreement in the slope estimate when groups are treated as random vs. fixed in a mixed model

I understand that we use random effects (or mixed effects) models when we believe that some model parameter(s) vary randomly across some grouping factor. I have a desire to fit a model where the ...
17
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1answer
15k views

Incidental parameter problem

I always struggle to get the true essence of the incidental parameter problem. I read in several occasions that the fixed effects estimators of nonlinear panel data models can be severely biased ...
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4answers
10k views

Fixed effect vs random effect when all possibilities are included in a mixed effects model

In a mixed effects model the recommendation is to use a fixed effect to estimate a parameter if all possible levels are included (e.g., both males and females). It is further recommended to use a ...
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4answers
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How to keep time invariant variables in a fixed effects model

I have data on a large Italian firm's employees over ten years and I would like to see how the gender gap in male-female earnings has changed over time. For this purpose I run pooled OLS: $$ y_{it} = ...
15
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4answers
580 views

How can I improve my analysis of the effects of reputation on voting?

Recently I had done some analysis of the effects of reputation on upvotes (see the blog-post), and subsequently I had a few questions about possibly more enlightening (or more appropriate) analysis ...
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3answers
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Concepts behind fixed/random effects models

Can someone help me to understand fixed/random effect models? You may either explain in your own way if you have digested these concepts or direct me to the resource (book, notes, website) with ...
14
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3answers
5k views

Removing factors from a 3-way ANOVA table

In a recent paper, I fitted a three-way fixed effects models. Since one of the factors wasn't significant (p > 0.1), I removed it and refitted the model with two fixed effects and an interaction. I'...
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1answer
11k views

When is it necessary to include the lag of the dependent variable in a regression model and which lag?

The data we want to use as dependent variable looks like this (it is count data). We fear that since it has a cyclic component and trend structure the regression turns out to be biased somehow. We ...
13
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2answers
227 views

What is the Frequentist definition of fixed effects?

Bolker (2015) writes on p. 313 that Frequentists and Bayesians define random effects somewhat differently, which affects the way they use them. Frequentists define random effects as categorical ...
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1answer
1k views

Standardized dependent variable within a group in panel data models?

Does standardizing of a dependent variable within the identifying group make sense? The following working paper (Deforestation slowdown in the Legal Amazon; Prices or Policies?, pdf) uses a ...
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3answers
5k views

When is a fixed effect truly fixed?

Consider a linear unobserved effects model of the type: $$y_{it} = X_{it}\beta + c_{i} + e_{it}$$ where $c$ is an unobserved but time-invariant characteristic and $e$ is an error, $i$ and $t$ index ...
12
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2answers
14k views

Difference-in-differences with individual level panel data

What is the correct way to specify a difference in difference model with individual level panel data? Here is the setup: Assume that I have individual-level panel data embedded in cities for multiple ...
12
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3answers
5k views

Is the Mundlak fixed effects procedure applicable for logistic regression with dummies?

I have a dataset with 8000 clusters and 4 million observations. Unfortunately my statistical software, Stata, runs rather slowly when using its panel data function for logistic regression: ...
11
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2answers
16k views

Why do random effect models require the effects to be uncorrelated with the input variables, while fixed effect models allow correlation?

From Wikipedia There are two common assumptions made about the individual specific effect, the random effects assumption and the fixed effects assumption. The random effects assumption (made in a ...
11
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1answer
24k views

difference-in-differences with fixed effects

I have two questions related to having fixed effects in the DD model. I have a treatment that occurs at different times (e.g., 2001, 2005, etc.). I want to fit a DD model, so I standardize the ...
10
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5answers
4k views

Bootstrapping hierarchical/multilevel data (resampling clusters)

I am producing a script for creating bootstrap samples from the cats dataset (from the -MASS- package). Following the Davidson ...
10
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1answer
56k views

How to deal with omitted dummy variables in a fixed effect model?

I am using a fixed effect model for my panel data (9 years, 1000+ obs), since my Hausman test indicates a value $(Pr>\chi^2)<0.05$. When I add dummy variables for industries that my firms ...
10
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1answer
53k views

Panel Data: Pooled OLS vs. RE vs. FE Effects

We had some discussion about the usefullness of Pooled-OLS and RE Estimators compared to FE. So as far as I can tell, the Pooled OLS estimation is simply an OLS technique run on Panel data. Therefore ...
9
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3answers
18k views

Difference between fixed effects dummies and fixed effects estimator?

I started to read about panel regression models. However, I am a bit confused about the different model specifications in the fixed effects model: Does a fixed effects panel regression always mean ...
9
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2answers
489 views

What is the best way to estimate the average treatment effect in a longitudinal study?

In a longitudinal study, outcomes $Y_{it}$ of units $i$ are repeatedly measuret at time points $t$ with a total of $m$ fixed measurement occasions (fixed = measurements on units are taken at the same ...
8
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1answer
19k views

How do I interpret a “difference-in-differences” model with continuous treatment?

How do I interpret the ATE coefficient (i.e., the post-treatment indicator interacted with the continuous variable)? Does it make sense? Should I break it down into subgroups and just run a fixed ...
8
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1answer
7k views

Specification of panel data

I am trying to find out the best specification for my dataset. I am trying to probe the effectiveness of the special economic zones in Poland in the meaning of growth of the economy in three ...
8
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1answer
784 views

How to use the Hausman test for gender discrimination?

I am trying to estimate the gender wage gap for male and female office workers in a large Swedish company to test whether there is gender discrimination. The Hausman test rejects the null that the ...
8
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1answer
25k views

Difference between one-way and two-way fixed effects, and their estimation

Consider a basic linear unobserved effect panel data model, e.g.: $$Y_{it}=\beta x'_{it}+c_i+\lambda_t+u_{it}, \quad t=1,\dots,T$$ where the vector $x_{it}$ contains the independent variables and $u_{...
8
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1answer
130 views

(References) How to derive experimental design models, instead of just memorize them?

In the M.S.-level Statistics Methods class I am taking, I've learned about various linear models for experimental design. Take, for example, $$Y_{ij} = \mu + \beta_i + \tau_j + \varepsilon_{ij}\,,$$ ...
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1answer
3k views

Interpreta​tion of main effect when interactio​n term is significan​t (ex. lme)

As an example I use Pinheiro, J. C. & Bates, D. M. 2000. Mixed-effects models in S and S-PLUS. Springer, New York. page 225. Rats whose body mass has been measured are fed by 3 different diets ...
7
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3answers
6k views

panel data - within-group estimate - individual fixed effects retrieved

I am analyzing panel data. First, I have to decide whether to use a random or fixed effect estimator. The Hausman test suggests to use the fixed effect estimator (also named within group estimator). ...
7
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3answers
5k views

What are the differences between the linear regression and mixed models?

What are the key differences between the following two models? ...
7
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1answer
26k views

First differences vs. fixed effects model for panel data

I'm aware of the fact that first differences and fixed effects are both designed for the same solution -- removing unobserved unit-level effects. However, I'm unclear on what happens when you include ...
7
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1answer
1k views

Real motivation for using mixed effect models, and when to use them and when not to

My question might sound naïve, but despite my internet search, I wasn't able to find a satisfactory answer. I've been introduced to linear regression, linear fixed effect and linear mixed effect ...
7
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2answers
3k views

Zero-inflated two-part models for semi-continuous data

I am trying to study predictors of companies' pollution output of some specific chemicals. The data I am using have many 0's (i.e., the company did not pollute at all with those chemicals) and then ...
7
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1answer
2k views

Dealing with hierarchical (panel, multi-level) data and fixed effects in LASSO?

The question pretty much explains itself. When running a Lasso regression on a lot of indexed (say by time and location) explanatory variables, is it best practice to transform all data using a ...
7
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0answers
5k views

Panel regressions with an interaction term between a time dummy variable and a time invariant variable

I have estimated the coefficients of the following equation, using the fixed-effect model: $Y_{it}=\alpha _i+ \rho _t + \beta _1 X_{it}+\beta _2 C_i*D_t+\epsilon_{it}$ I have observations from 1980 ...
7
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1answer
4k views

Difference-in-difference in panel data

Under which conditions should we expect the difference-in-difference estimate to be equal to the equivalent panel data model? Strictly speaking, whenever we have a experiment that offers a well ...
6
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3answers
7k views

What is the intuition on fixed and random effects models? [duplicate]

Now I'm having a hard time having a grasp on the difference between fixed and random effects of regression models. I believe I understand it's recommended to use random effects if you consider ...
6
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1answer
14k views

Difference between fixed effects models in R (plm) and Stata (xtreg)

I'm trying to re-create an analysis done using Stata function xtreg (though I don't have the code) with ...
6
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1answer
2k views

Are the relations in fixed, random and mixed effect models and multilevel models causal?

In fixed, random and mixed effect models, and multilevel models, the response random variable is represented as a function of some explanatory variables and random errors. I was wondering if the ...
6
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1answer
5k views

cluster-robust standard errors are smaller than unclustered ones in fgls with cluster fixed effects

I'm currently working on some experimental data. The experimental design consists of two treatments. In each treatment, 20 subjects are randomly matched in pairs and participate to a simple game. The ...
6
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1answer
292 views

Three way fixed effects vs combining two of the effects

I have panel data on employment that varies by year, sector and location and thus would like to run a fixed effects regression considering these 3 dimensions. The issue is that I use R and the ...
6
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2answers
2k views

Why does a fixed-effect OLS need unique time elements?

The plm function of the plm library in R is giving me grief over having duplicate time-id couples, even when I'm running a model ...
6
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1answer
4k views

Hausman test: the larger the sample the more significant the Hausman test statistic?

Hausman test statistic formula: $$ H=(\beta_{f}-\beta_{r})' \left[\mathrm{Cov}(\beta_{f})-\mathrm{Cov}(\beta_{r})\right]^{-1}(\beta_{f}-\beta_{r} ) $$ where $\beta_{f}$ is the beta of fixed effects ...
6
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2answers
261 views

Why is it valid to account for k-1 intercepts w/ only 1 random intercept parameter?

I possess a basic understanding of random vs. fixed effects, and how to code random effects models in SAS. However, I'm having trouble wrapping my head around the derivation of random effects terms, ...

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