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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287
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9answers
540k 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?
167
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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 ...
51
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2answers
41k 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
41k 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
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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
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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. ...
21
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3answers
38k 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 ...
18
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2answers
31k 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 ...
18
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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 ...
15
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4answers
9k 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 ...
15
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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
576 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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1answer
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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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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 ...
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3answers
4k 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 ...
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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
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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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3answers
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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: ...
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2answers
15k 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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2answers
12k 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 ...
10
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1answer
55k 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 ...
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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 ...
9
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2answers
410 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
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
746 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
21k 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 ...
8
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1answer
116 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, $$Y_{ij} = \mu + \beta_i + \tau_j + \varepsilon_{ij}\,,$$ ...
8
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1answer
47k 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 ...
8
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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 ...
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3answers
16k 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 ...
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
17k 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 ...
7
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1answer
25k 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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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 ...
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3answers
5k 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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3answers
5k 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). ...
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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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
260 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, ...
6
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1answer
6k views

Model selection in mixed-model context using lmer

Assume I have two factors A and B potentially predicting my outcome Y. Now I would like to test for fixed-effects using likelihood ratio test to find the best model. ...
6
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1answer
977 views

FGLS and time fixed effects

Context: I am performing growth regressions on a panel data set in R, including individual- and time fixed effects. Estimating with OLS delivers results that seem to suffer form serial correlation. ...
6
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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 ...
6
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1answer
3k views

group fixed-effects, not individual-fixed effects using plm in R

I am analyzing some data to evaluate the impact (causal effect) of a program that is delivered at group level (a village). The outcome of interest is measured at the individual level (individuals ...
6
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1answer
94 views

Where are the Wald p-values and where are the LRT ones in the resulf of mixed models? [closed]

I read, that there are many methods of determining the degrees of freedom, thus calculating the p-values for fixed effects in mixed models. I read, that the worst is the Wald test and the Log-...
6
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1answer
301 views

Hausman-Newey test for serial correlation in Poisson with Fixed Effects

The article from Hausman, Hall, and Griliches (1984) "Econometric Models for Count Data with an Application to the Patents-R&D Relationship" has become the canonical example for conditional MLE of ...

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