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 ...
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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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Are the level-level and log-log models nested?

In my Econometrics Textbook, It says that an F-test (RESET test in this case) can be used to check for misspecification in the following models: $$ Y = \beta_{0} + \beta _{1}x_{1} + \beta _{2}x_{2} + \...
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Not sure of model choice - significant p-values but very low R2 adj

I am writing a thesis in which I'm trying to see what the relationship is between how innovative a patent is (as determined by a series of measures based on NLP that) and the financial value of that ...
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Changing relation between independent and dependent variable over time

I am currently trying to run a linear regression model where the effect of one of my independent variables (Xit) on my dependent variable (Yit) changes over time. Specifically, I suspect the ...
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Pols vs FE panel data l clustered l Model specification

I would be very thankful to have your insight regarding the equation of the estimation models below, and if you can help in clarifying the doubt explained below. In this research, data was retrieved ...
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Do insignificant variables result in a specification error?

I am trying to understand omitted variable bais better. I know that it detects irrelevant variables, but are irrelevant variables and insignificant variables synonymous here? If I have a regression ...
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Model specification of Linear Mixed effect model

I've got data with which I am trying to find causality of a dependent variable "relative growth rate" of corals on different types of reefs. The data originate from an unbalanced design, ...
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The exact meaning of "correctly specified"

I will cite a paper I am reading: (Bugni, Federico A., Ivan A. Canay, and Xiaoxia Shi. "Specification tests for partially identified models defined by moment inequalities." Journal of ...
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The exact meaning of specification tests

I thought that a specification test is a test that attempt to check whether a regression model's specification (such as linear and quadratic) is correct or not. However, recently I am facing many ...
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Concerns about pre-trend stability testing

In this discussion, @Thomas Bilach well explains the equation to test pre-trend stability. $$ y_{kt} = \alpha_k + \lambda_t + \delta_{-2} d_{k,t-2} + \delta_{-1} d_{k,t-1} + \delta d_{kt} + \delta_{+1}...
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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 ...
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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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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 ...
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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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Question about regression using a rate vs a count as the dependent variable

Let's say I wanted to run a regression of mortality on an x variable, so I could see 3 different possibilities I can do I define a rate: $y = \left(\frac{\#deaths}{population}\right)$ and regress $$...
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Bayes estimates and model misspecification

Consider a misspecified model: $$P \sim \text{SegmentedUniform}(0,1) \\ Y \mid P \sim \text{Binomial}(N,P).$$ Where SegmentedUniform has uniform density on intervals $$(0.1, 0.2), (0.3, 0.4), (0.5, 0....
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Event Study with two treatments

Lets say I wanted to include two different treatments in a diff in diff at the same time, so I could have: $y_{i,t} = \lambda_i +\tau_t + Treat1_i*post_t+Treat2_i*post_t + \eta_{i,t}$, where $\...
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Role of misspecification by biased data in the generalization error

I am confused with the role that model misspecification plays in the generalization error, in particular when the misspecification is due to a biased (non representative) training dataset. To clarify ...
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Consequences of choosing the wrong GLM response distribution

In Chapter 10 of McElreath's Statistical Rethinking (2nd edition), he argues that the response distribution for a GLM should be chosen to maximize entropy given a set of constraints on the response ...
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Practical numerical example illustrating how bayesian p-values should be used for model checking?

Can you give a practical numerical example illustrating how bayesian p-values should be used for model checking?
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3 answers
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Bayesian inference with false models: to what does it converge?

This is the second follow up question from these two previous questions: Bayesian inference and testable implications How do I perform an actual "posterior predictive check" in this model? ...
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How do I perform an actual "posterior predictive check"?

This question is the follow-up of this previous question: Bayesian inference and testable implications. For concreteness, consider the following bayesian model. This model is not to be taken ...
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How bad are short-term forecasts of ARIMA models of ARFIMA processes?

Suppose I have a set of economic time series that appear to be a unit root process. I difference them, and fit an ARMA model to the differenced series. Suppose however that the true data generating ...
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Bayesian model averaging when none of the models is well specified

Usually, from what I've read of Bayesian Model Averaging (BMA), a typical assumption is that one of the models is well specified... However, what will happen when all models are misspecified? What ...
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SEM: Why is there no dependable connection between the size of SEM residuals and the type or degree of model misspecification?

Kline (2016) p. 278 writes [Y]ou should know that there is actually no dependable or trustworthy connection between the size of the residuals and the type or degree of model misspecification. For ...
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Are there any practical differences in fitting a random slope vs. fitting an interaction term in the intercept in lmer

I am trying to fit a few models with the form ...
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Buld prediction intervals for glmmTMB

I'm using glmmTMB to build a mixed effect logistic model from which I want to draw predictions. The predict() function applied to a glmmTMB model allows extracting the ML prediction and the relative ...
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Path analysis model fit statistics. RMSEA = 0.106

Hi folks, My path analysis is using primary data that I've collected for a uni project. After removing the very non-signif variables, I have a model (which I hypothesised) that seems to work pretty ...
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how to interpret the smoothed effect of time in GAMM models

I have recently taken a plunge into the world of Generalized Additive Mixed Models (GAMMs) after learning that including the quadratic and cubic fixed and random effects of time to understand students'...
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Over "specification" of a statistics model?

For a simple example, I am fitting data with a likelihood function generated by a normal distribution. The first model is the normal distribution with two-parameters. The second competing model is the ...
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Non-Linear regression and variance misspecification

Given a non-linear regression model for cross-section data $$y_i = f(x_i,\theta_0) + \epsilon_i,$$ where it is assumed that $\mathbb E[y_i\lvert x_i] = f(x_i,\theta_0)$, I understand that it is a ...
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2 votes
2 answers
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$R^2$ is too high- reasons? [closed]

What are the reasons of too high values of $R^2$? I only know that its value increases when the number of independent variables increases. What are the other factors?
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Question on econometric specifications transformation [closed]

Two groups of forecasters are trying to forecast outcome variable y by issuing forecast X. Denote the two groups of forecasters with Z={1,2}. We want to know whether group 1 is more accurate in ...
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Bayesian inference with simple models and many data points: impact of priors and the number of data points

The setting. Let us assume I would like to perform Bayesian inference for a low-dimensional model on a large dataset, i.e., there are many more data points than there are parameters to identify. Let ...
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When regularizing based on an informative prior, how to give model a little more freedom to partially reject regulariziation

I am new here I hope this question is appropriate. I am modelling a spatial domain, whereby I have repeated measures at n locations. I make a bayesian linear model at each n locations based on about ...
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2 votes
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Random effects for mutually inclusive grouping factors

I am trying to fit a model on a set of data (e.g. 10,000 observations with 20 explanatory variables). The observations belong to 30 groups, G1, G2, G3, ... G30, so I need to account for the grouping ...
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Relative importance different model diagnostics in LMM/GLMM

I may be over thinking things but I have been stuck on this issue for the last few days. I am currently modelling data with a large number of clusters but cluster size is limited to 2, with a skewed ...
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Endogenous selection bias / d-separation in SEM (Structural Equation Modeling)

I am a psychology student and currently working on a paper about omitted-variable bias in structural equation modelling (SEM). I am trying to tie endogenous selection bias to parametric SEM to ...
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Does a high Chi square p-value for a whole model mean it is insignificant if likelihood ratio tests indicated variables should be added?

I've been estimating lots of versions of the same model by incrementally adding variables. With some variables, if I add them to the model, the likelihood ratio test indicates that they are ...
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3 votes
1 answer
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Why does $\mathbb{E}[s^2] \geq \sigma^2$ if we omit relevant variables (linear regression model)?

Suppose that the "true" model is $Y = X\beta + Z \gamma + \varepsilon$ with the standard assumptions of the linear model. However, we only perform an OLS-regression on the variables contained in $X$. ...
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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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