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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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25 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 ...
41 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 ...
20 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 ...
74 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 ...
84 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 $X$. ...
9 views

Correct Specification for Censored Data

I have some construction data, which shows the starting year of unfinished and finished projects but don’t have any information on the completion time of finished projects. If I had data on the ...
18 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 ...
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 ...
51 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 ...
74 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 ...
39 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 ...
67 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)). ...
212 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-...
311 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 ...
50 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 ...
64 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 ...
37 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 ...
204 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 ...
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 $f$ ...
31 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 ...
73 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 ...
63 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 ...
397 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 ...
192 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 ...
102 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 ...
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 ...
567 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 ...
4k 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 ...
268 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 ...
124 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 ...
191 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 ...
305 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 ...
57 views

How to compute the likelihood when uncertain about underlying distribution

In a Bayesian approach, when I have no previous idea about the likelihood of a given event, can I simply gather a lot of data and use that distribution as my likelihood (1) and as I gather more and ...
2k views

Statistical test to determine if a relationship is linear?

What is the best statistical test to use if I measure the value of $Y$ (e.g. pH) for specific values of $X$ e.g. $X=0,10,20,30,...,100$ (e.g. temperature) and I want to test weather the relationship ...
101 views

Logistic Regression - confused about one independent variable

I have a question regarding a binary logistic regression. Its about the plausibility of the influence of one independent variable. I am analyzing the influence of the size of a farm on the use of ...
1k views

regression of a level vs a change variable

This question has likely been asked already but due to the lack of proper terminology I might not have been able to find google up the relevant questions. We have data for several years: 2000, 2001, ....
97 views

Some logical questions about parameter estimation in the situations when the model is misspecified

When we have a parametric model, we can use many procedure to estimate the parameters in the model, i.e., obtain many different estimators. We usually focus on the set of consistent estimators. For ...
19 views

A Game Plan for Cross-Section Modelling

Imagine we have already built our linear regression model, with a certain dataset. Which order of tests would you follow to be sure that whatever conclusions you may want to extract are correct? For ...
229 views

Joint significance test before or after hettest in Stata?

I ran an OLS regression in Stata, then a hettest, and there is heteroskedasticity in the X variables. So I threw on a ,robust to ...
874 views

Central limit theorem for maximum likelihood estimators when modelling assumptions are violated

Lehman's Element's of Statistical Learning Theory gives in Theorem 7.5.2 a central limit theorem for multiparamter maximum likelihood estimators. (Many other sources provide similar theorems.) The ...
290 views

Using asymptotic distribution under the null when the null hypothesis is false

This is a general question about hypothesis testing in statistics. A standard hypothesis test as I see it is based on 3 things: Stating a null hypothesis Computing a test statistic for the ...
518 views

Comparing Classical and Robust (Huber-White/sandwich/heteroscedasticity consistent) Standard Errors in Linear Multiple Regression

I'm running a linear multiple regression model of the type $y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \beta_3 X_{i3} + u_i$. I came across King and Roberts' 2015 paper called "How Robust ...
237 views

Statistical Inference Under Misspecification

The classical treatment of statistical inference relies on the assumption that that a correctly specified statistical is used exists. That is, the distribution $\mathbb{P}^*(Y)$ that generated the ...
104 views

Parametric cdf or empirical distribution function?

Say I have a set of i.i.d. data and want to learn about the data generating distribution (the cdf would suffice). I could then fit various different suitable parametric models via say maximum ...
3k views

Conditional vs. Marginal models

I have data with an outcome of 0 or 1 (binary) representing success or failure. I also have two comparison groups (Treatment vs. Control). Each subject in the study contributed 2 observations (the ...
334 views

Using simulated data to check when patterns in GLMM residual plots are acceptable

I have run the following Poisson GLMM: ...
286 views

Problems due to analyzing variables from different levels at one single level

Please ease the following paragraph from the first chapter , Introduction to Multilevel Analysis , p.3 of the book: Historically , multilevel problems have led to analysis approaches that moved all ...
112 views

Recommend monograph on statistical model misspecification

Is there a good book on statistical model misspecification in general? It should cover, for example, the behavior of estimators (e.g., maximum likelihood) when the specified parametric family does not ...