# Questions tagged [misspecification]

Problems with model specification, such as missing variables/predictors, wrong functional form, wrong variance or covariance structure, etc.

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### Linktest results interpretation

Linktest's rule of thumb is _hat should be statistically significant while _hatsq should not be significant, in order for the model to be called "correctly specified". However, when I did ...
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### A misspecification error with linear models that can complete reverse the direction of an effect, has this been described, has this a name?

Linear models are ubiquitous in economic, social, health and nutritional sciences and the starting point for much research and many articles. However, there is a problem with linear models. When the ...
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### How to determine if LMER model is specified correctly given output?

I am running a mixed effects model using LMER. In the past I recall seeing groups represented in the summary output with brackets, for example condition[2] would correspond to condition labeled two in ...
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### Why are parametric models usually robust to mild misspecification?

Statisticians often use parametric families of models, for example normal distributions with unknown mean and variance. However, nothing in real life is perfectly normally distributed (or distributed ...
6 votes
4 answers
660 views

### What is the benefit of regression with student-t residuals over OLS regression?

Sometimes I see advice to fit regressions with student-t residuals rather than using OLS (which is equivalent to assuming normally distributed residuals) if the distribution of the residuals is heavy-...
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### What is the consequence of misspecification in logistic regression

In linear regression, the Ramsey RESET test can be used to test if the model is misspecified. The Gauss-Markov theorem allows us to understand the consequences of misspecification in linear regression....
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### Is traditional negative binomial regression robust to model misspecification or not?

By "traditional" NBR I mean NB2, i.e. the one modeling variance as a quadratic function of the mean, with the formula: $Var(Y)=E[Y]*(1+\alpha*E[Y])$. I have found contrasting statements in ...
2 votes
1 answer
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### Does the problem of multiple testing also apply to the testing of assumptions?

When dealing with statistical tests, sometimes we can run into cases where many assumptions would apply and consequently would need to be tested. In complex models, testing many assumptions at 5% may ...
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### Simple explanation of Takeuchi’s information criterion?

Takeuchi’s information criterion is said to be the generalization of AIC to misspecified models. That publication presents DEGREES OF FREEDOM FOR NONLINEAR LEAST SQUARES ESTIMATION. From that source: ...
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3 votes
1 answer
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### ARMA/GARCH statistical significance of estimated parameters

My question is general and is concerned with ARMA-GARCH modeling. When performing the joint estimation of the ARMA and GARCH parts, some works tend to not be concerned with the statistical ...
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### Wald Statistic Simplification - 2 Restrictions?

(Specify the wald statistic as: W=$(R\hat{\theta}-r)'[R\hat{V}(\hat{\theta})R']^{-1}(R\hat{\theta}-r)$ Where r is a vector of restrictions, R imposes the restrictions on $\hat{\beta}$, $\hat{\theta}$ ...
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### Issues in testing a simple linear relationship. Collinearity? Misspecification? Any other insight?

I have a theoretical model saying that Y should be equal to: Y = X + c * (W - X) + (Z1 - Z2), where c is a given constant. Here, it may be important to say that X is measured with error. Someone ...
1 vote
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### Misspecification in the outcome model with regression adjustment for propensity score?

The propensity score is a popular tool used to control for confounding by covariates $C$ on the effect of an exposure $A$ on an outcome $Y$. There are several ways to incorporate the propensity score ...
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### How can I use the distribution of run lengths to test if a sequence is generated from flips of a fair coin?

I have a very long sequence (in the tens of thousands) of binary outcomes from some data-generating process. I believe that these outcomes are iid Bernoulli trials with p = 0.5, equivalent to flipping ...
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### What is a good test for whether a sample is drawn from a particular parametric family against a generalized alternative

Suppose I have some large number n of draws from a strictly positive distribution that I believe to be a member of a particular parametric distributional family. I use the draws to estimate the ...
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