Fixed effects model

fixed effectsFixed effectFixed effects estimationFixed effects estimatorfixed effects factorfixed effects models
In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities.wikipedia
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Mixed model

mixed effects modelslinear mixed modellinear mixed models
This is in contrast to random effects models and mixed models in which all or some of the model parameters are considered as random variables.
A mixed model (or more precisely mixed error-component model) is a statistical model containing both fixed effects and random effects.

Random effects model

random effectsrandom effectvariance component
This is in contrast to random effects models and mixed models in which all or some of the model parameters are considered as random variables.
In econometrics, random effects models are used in the analysis of hierarchical or panel data when one assumes no fixed effects (it allows for individual effects).

Panel data

longitudinal datapanel(panel)
In panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means.
Two important models are the fixed effects model and the random effects model.

Durbin–Wu–Hausman test

Hausman specification testHausman testThe Hausman test, ''or'' Hausman specification test
The Durbin–Wu–Hausman test is often used to discriminate between the fixed and the random effects models.
The Hausman test can be also used to differentiate between fixed effects model and random effects model in panel data.

Fixed-effect Poisson model

* Fixed-effect Poisson model
Their outcome of interest was the number of patents filed by firms, where they wanted to develop methods to control for the firm fixed effects.

Statistics

statisticalstatistical analysisstatistician
In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities.

Statistical model

modelprobabilistic modelstatistical modeling
In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities.

Parameter

parametersparametricargument
In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities.

Econometrics

econometriceconometricianeconometric analysis
In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population.

Biostatistics

biostatisticianbiometrybiometrician
In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population.

Regression analysis

regressionmultiple regressionregression model
In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population.

Estimator

estimatorsestimateestimates
In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).

Coefficient

In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to refer to an estimator for the coefficients in the regression model including those fixed effects (one time-invariant intercept for each subject).

Omitted-variable bias

omitted variable biasomitted variablesomitted variable
Such models assist in controlling for omitted variable bias due to unobserved heterogeneity when this heterogeneity is constant over time.

Finite difference

difference operatorfinite differencesNewton series
This heterogeneity can be removed from the data through differencing, for example by subtracting the group-level average over time, or by taking a first difference which will remove any time invariant components of the model.

Efficiency (statistics)

efficientefficiencyinefficient
If the random effects assumption holds, the random effects estimator is more efficient than the fixed effects estimator. If the error terms u_{it} are homoskedastic with no serial correlation, the fixed effects estimator is more efficient than the first difference estimator.

Consistent estimator

consistentconsistencyinconsistent
However, if this assumption does not hold, the random effects estimator is not consistent.

Endogeneity (econometrics)

endogenousendogeneityreverse causality
Strict exogeneity with respect to the idiosyncratic error term u_{it} is still required.

Errors and residuals

residualserror termresidual

Controlling for a variable

controlcontrollingaccounted for
Since \alpha_{i} is not observable, it cannot be directly controlled for.

Multicollinearity

collinearitymulticollinearperfect multicollinearity
One is to add a dummy variable for each individual i>1 (omitting the first individual because of multicollinearity).

Homoscedasticity

homoscedastichomogeneity of variancehomoskedastic
If the error terms u_{it} are homoskedastic with no serial correlation, the fixed effects estimator is more efficient than the first difference estimator.

Autocorrelation

autocorrelation functionserial correlationautocorrelated
If the error terms u_{it} are homoskedastic with no serial correlation, the fixed effects estimator is more efficient than the first difference estimator.

Random walk

random walkssimple random walkRandom walks on graphs
If u_{it} follows a random walk, however, the first difference estimator is more efficient.

Minimum distance estimation

minimum distance rule
:which can be estimated by minimum distance estimation.