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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42 views

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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62 views

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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3answers
177 views

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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201 views

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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27 views

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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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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1answer
31 views

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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11 views

How does misspecification of a structural equation model impact the results or interpretation of the model?

Any ideas? I am new to SEM and am struggling to articulate why and how misspecification of the model affects results and interpretation of the SEM.
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72 views

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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57 views

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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1answer
69 views

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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2answers
65 views

$R^2$ 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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27 views

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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29 views

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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27 views

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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76 views

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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41 views

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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76 views

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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1answer
94 views

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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1answer
22 views

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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16 views

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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1answer
56 views

Finding SSE when ignoring a parameter in estimation

The model is $Y=XB+Zy+e$ where $B$ and $y$ are unknown parameters and $e\sim \text{N}(0,σ^2 I)$. Using ordinary least squares and ignoring $Z$ in parameter estimation, I need to find the distribution ...
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1answer
24 views

Does it make any sense to apply a GETS modeling algorithm to a panel?

Let's assume to have a panel including observations for 88 individuals over 18 years (1584 observations). The panel is now populated with a broad set of 50 possible regressors that I would like to now ...
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1answer
105 views

Partial or incomplete Bayesian update

In Bayesian statistics, usually we have some prior distribution $P(M)$, some observations $X$, and we compute a posterior $P(M|X)$. The observation allows us to gain information about the generating ...
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42 views

Misspecified regression & asymptotics

Consider the weighted regression coefficient $\hat{\beta} = (X'WX)^{-1}X'WY$ where the regression is possibly misspecified and $W$ is known. Let $\beta_* = (E[X'WX])^{-1}E[X'WY]$ and the related ...
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85 views

How to solve a well fitted model - Model Misspecification

I am currently writing a paper, analysing the impact of goldprice movements on the capital structure of gold mining firms. My basic model is a simple OLS model with (y=leverage and x=ln(goldprice)). ...
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1answer
293 views

Robust error estimation and hazard ratio with non-proportional hazards

I recall having heard that the hazard ratio, estimated in a Cox model, can be made robust against the parallel hazard functions assumption. The key to this is using a Huber-White, or Huber-Eicker-...
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1answer
551 views

How to calculate sandwich standard errors for generalized least squares models?

Dependent data can be modeled using covariance structures like compound symmetry, spherical, AR-1, and other. Using generalized least squares, inference can be made on the regression coefficients ...
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1answer
82 views

Conducting sub-sample analyses with propensity score adjustment when propensity score was generated on the whole sample

I am analysing data from an open cohort and because there is a selection bias associated with the exposure, I calculated the propensity score (PS) and used it as covariate in my regression model (PS ...
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1answer
79 views

Omitted Variables and Endogenity

I am currently trying to figure out the problem of endogenity, which occurs when an explantory variable is correlated with the error term. There are apparently different causes for endogenity, but one ...
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40 views

Modelling costs with correlated response variables

Say I have a data set with the following measures Number of vacation days (NumDays) Accommodation costs (Accom) Total Drinks costs (Drinks) Total Meals costs (Meals) Total Travel costs (Travel) Total ...
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1answer
271 views

Does having a result that is “robust to specification” make it more likely to be true?

I'm wondering if there is any evidence (simulated or otherwise) demonstrating that robustness to specification actually means a result is more likely to be true. By robustness to specification I mean ...
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1answer
57 views

How to correct inference for searching over multiple specifications?

Correcting for multiple testing is easy, and there's a lot of literature around it. But now consider a different problem. Say you have $X$ and $Y$ and you want to estimate $E[Y|X=x]= f(x)$ where $f$ ...
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33 views

Fredrick Taylor Inspired Optimization for Shovel Loads

Premise In Taylor's original Principles of Scientific Management, the optimal weight of a single shovel load was calculated (roughly 21 pounds). This had some interesting implications: short of this ...
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1answer
86 views

Correct model specification and pre-specification: Is this problem solved in Bayesian statistics?

In frequentist statistics, the validity of the inference depends on the assumption that the model is correctly specified as well as pre-specified. Violations of these assumptions (i.e. we only specify ...
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0answers
76 views

RESET test and AIC

What is the difference between Ramsey regression equation specification error test (RESET) test and Akaike information criteria (AIC)? From wiki, it says RESET "test whether non-linear combinations ...
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1answer
462 views

Lasso for variable/feature selection in binary response data

If we want to conduct variable selection for a high-dimensional data with the binary responses, one good solution will be using L1 regularized logistic regression. However, I wonder what will happen ...
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1answer
243 views

Effects of model selection and misspecification testing on inference: Probabilistic Reduction approach (Aris Spanos)

This question is about pre-test bias, inference after model selection and data snooping within the Probabilistic Reduction (PR) methodology by Aris Spanos (which is related to the Error Statistics ...
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0answers
131 views

Comparing Combinations of Regressors for Linear Regression Feature Selection

I'm trying to make a time series linear regression for forecasting purposes. I have picked eight features that logically are tied to the independent variable (separate time series data sets). I ...
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11answers
8k views

Why should I be Bayesian when my model is wrong?

Edits: I have added a simple example: inference of the mean of the $X_i$. I have also slightly clarified why the credible intervals not matching confidence intervals is bad. I, a fairly devout ...
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1answer
705 views

residuals increases with fitted values : what kind of model misspecification might it indicate?

As we know, plotting residuals against fitted values may indicate whether the model is misspecified or the variance is not constant, or both. Let's focus on model misspecification only and set aside ...
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2answers
5k views

Is it true that Bayesian methods don't overfit?

Is it true that Bayesian methods don't overfit? (I saw some papers and tutorials making this claim) For example, if we apply a Gaussian Process to MNIST (handwritten digit classification), but only ...
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2answers
317 views

Statistical inference under model misspecification

I have a general methodological question. It might have been answered before, but I am not able to locate the relevant thread. I will appreciate pointers to possible duplicates. (Here is an excellent ...
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0answers
141 views

Marginal standardization with robust error estimation for estimation of risk ratios

I've been using software to calculate multivariate risk ratios from logistic regression models. The basic premise is to predict the risk in everybody with some exposure and then again with the ...
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0answers
211 views

Maximum likelihood estimation for incorrect distribution parameter

Supposing I have a random variable $X$ with distribution $$f(x | \boldsymbol{\theta}, \boldsymbol{\varphi}).$$ Here $\boldsymbol{\theta} = (\theta_1,\theta_2,...,\theta_r)$ are $r$ parameters which ...
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1answer
327 views

Experimental design before and after with control group

I have a project which test effectiveness of two factors (two levels, receive and not receive the factor). There are three stage consecutively through time, and the factors are imposed in the second ...