Questions tagged [goodness-of-fit]

Goodness of fit tests indicate whether or not it is reasonable to assume that a random sample comes from a specific distribution.

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Comparing return distributions

Taking the log and/or normalizing (subtracting the mean and dividing by the standard deviation) stock returns still does not eliminate the dependence or heterogeneity. E.g. I cannot assume that each ...
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goodness of fit statistic independant of the fixed effects

I am using glm model to fit data. I want to check if my fit is good. My model is usually the classical model with only fixed effects. In order to do so, I use goodness of fit tools like residual ...
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Can you compare fitness of a data set to a predetermined/expected line?

I have a experimental data of counting the timing of events which, if random, should follow a Poisson distribution. To evaluate whether this is true I plotted the standard deviation of the data ...
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Goodness of fit using characteristic function

When assessing goodness of fit of a model, one can use, for example, a Q-Q plot of empirical vs theoretical distributions. But how does one perform a GoF assessment when there is no closed form ...
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p value for the Cramér–von Mises two sample test in python [closed]

Where can I find a package that computes the p-value for the Cramér–von Mises 2 sample test in Python. I was able to find a package that computes the Cramér–von Mises 2 sample test itself : https://...
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Goodness of Fit ot Least Squares with known measurement uncertainty

We want to estimate $\beta$ for $$ y = x\beta + \epsilon $$ where $y$ and $x$ are $n\times 1$ vector and $\epsilon$ is not i.i.d, but $\epsilon \sim N(0, \sigma^2\Omega)$, where $\Omega$ and $W$ are $...
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How to interpret Hosmer and Lemeshow test in R?

I'm reading some researches about how to use Hosmer-Lemeshow Goodness of Fit (GOF) Test in R. The results are quite clear and reasonable: X-squared, Degree of Freedom, p-value,.. However when I take a ...
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$R^2$ of regression of unity on $X$ (i.e. $Y$ is a vector of ones)

Assume we have a vector of ones and some (one or more) variables $X$, and we run a linear regression of unity on $X$ (i.e. if we only assume one RHS variable, the implied scatter plot would be a flat ...
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RMSE normalization. Number of bins

I am using RMSE (Root mean squared error) as a measure of goodness of fit. I am fitting a formula to binned data. The number of bins is not fixed: if there are less than 5 data values in a certain bin,...
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Koenker & Machado (1999) goodness-of-fit criterion (R1)

Has anyone come across a journal paper or a book providing a rule of thumb regarding what R1 is appropriate in research that focuses on the impact of macroeconomic or bank-specific variables on bank ...
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Applying bootstrapping to test if the data followed a certain distribution

I have a dataset with a large sample size (around 80,000). I would like to test if the data followed a certain distribution. I can fit a distribution function, such as log-normal or gamma, to the ...
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Comparing two discrete paired datasets

The problem: I am studying the estimated number of cases of malaria in regions of the world and found that both the WHO and IHME have their own estimates. I want to find if the difference between the ...
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How to compute $R^2$ of test set in leave-one-out CV?

In leave-one-out cross validation, at each iteration, my test set is composed by only one data point - precisely the "left out", to be compared with the predicted one, using the estimated coefficients ...
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Using Cross Validation for Goodness of Fit for Competing Inferential Models

I have a project where I need to 1) perform inference: understand the role of predictors on the response through models (with my data I need to choose a model where I can reasonably assess how changes ...
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How to test that a subset of data is distributed no differently than original (discrete, not normal)

In the research I am doing we have initially had ~600 samples which had a certain distribution (not normal, although close). The characteristic of these samples that I am interested in is discrete (...
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Why McFadden's pseudo-R^2?

Why can't we simply use ordinary $R^2$ in logistic regression, as we do in linear regression? Domencich and McFadden seem to imply that heteroskedasticity is an issue: but I don't understand why. In ...
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Highly fluctuating value of test statistic in Anderson Darling test

I am trying to verify whether my sampled data is from a population with a Gamma density function. My plan is to do this by means of the Anderson-Darling test. Before doing so, I thought it would be ...
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Sum of pure errors

We know that in a simple linear regression model that the sum of all the residuals is 0 but why is it that the sum of all the pure errors is also 0? Is there a relation between them?
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Ridge regression and low R-squared

I am currently working with a strongly balanced data set. I have 15 countries over the period 1990-2017. My dependent variable is CO2 emissions. My independent variables are GDP per capita, total ...
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What is a good metric for a binary classifier when we are more interested in Precision than Recall but care about confidence scores?

I have an heavily imbalanced dataset and am training a binary classifier (which produces scores in the range 0 to 1) and need a single summary metric to tune hyperparameters with. For my problem, ...
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How to compare AIC and goodness of fit tests?

My data is categorical. I have fitted two models, say, model 1 and model 2. Model 1 is larger than model 2 (in terms of the number of estimated parameters) and model 2 is nested within model 1. AIC ...
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Height of fitted distribution much higher than real data

For what reason can the height of a fitted distribution be much has higher than the real data it was fitted on? Does it just mean that the distribution does not fit the data or that I have too few ...
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Statistical test to detect regional excess of observations compared to background observations

I have data on the protein position of genetic variants. I want to determine whether there is a region of the proteins with a significant excess of variants relative to controls. Consider this ...
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Zero inflated generalized poisson: How can I compare 2 models?

I'm using Statsmodels to fit count data by Zero Inflated Poisson Regression. Suppose that I have 2 models: ...
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Goodness of fit with observed and estimated data

I am trying to fit a model to some data. It represents how density decreases with radius. The model or profile is exponential. I wanted to apply some goodness of fit test. I tried with the chi-square ...
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Can we apply the Probability Integral Transform to Dependent Random Variables?

Let's suppose we deal with a non-homogeneous Poisson process having intensity function λ(t), t ≥ 0. The event times X1, X2, … of ...
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How to decide between goodness of fit tests

I have a question on BIC and AIC. I have a data set and I need to test this data set if it fits various distributions (for example, Gamma or Poisson, etc.) I need to use AIC and BIC statistics for ...
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What is going on when deviation is significant but then not significant for outlier test using DHARMa?

I've used the DHARMa package to determine if my model fit is acceptable. I have run the following model: Number of types of bird food ~ number of feeders, age, education, bird feeding years. I've ...
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P-value for goodness of fit test

I have a test statistic of 0.533208 for a chi-square distribution with degrees of freedom =2.When I calculate the P-value, it automatically gives me p-value for right tail(0.766)and for left tail(0....
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OLS regression fit

I have 5 data sets fitting exactly the same ols model y = 5 + 0.4x. What is the best way to assess model's goodness of fit for each of the dataset and determine whether to use that model ?
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Convergence rate of test-statistic to chi-square distribution

I know that the to test whether $\Sigma=\Sigma_0$ against $\Sigma\ne\Sigma_0$ for an $n\times p$ data matrix, the test statistic is $np(a-1-\log g)$ where $a$ and $g$ are the AM and GM of the eigen ...
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Can the Chi-Square Value be Used to Quantitatively Discuss Goodness of Fit for any Data?

To quantitatively discuss the relationship between experimentally measured results and a fitted curve, is obtaining the Chi-Square value for my data relevant? By that I mean if I obtain the Chi-square ...
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In a linear regression, trying to show $R^2 = r_{xy}^2$ using projections / geometric intuition

In a linear regression $$ Y = X\beta + \varepsilon, $$ I define two (standard) projection matrices. The projection matrix into subspace spanned by columns of the design matrix $X$: $$ H := X(X^\top ...
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Chi Square test gives bad results for good gaussian fit

I have a set of data, that I wanted to fit with the sum of 3 Gaussians. The data can be fit well: However, as can be seen, my p-value is 0.00. Can someone explain me, why? The code, that I used for ...
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What does goodness of fit tell us with skewed data?

"The goodness of fit test is a statistical hypothesis test to see how well sample data fit a distribution from a population with a normal distribution. Put differently, this test shows if your sample ...
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Multivariable residual analysis and goodness of fit

I am reading the paper Statistical Modeling: The Two Cultures (2001) by Leo Breiman. In section 5.2 he claims: Residual analysis is similarly unreliable. In a discussion after a presentation of ...
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How to combine/pool the standard error of fitting parameters from multiple fits of the same model?

Let me first explain the context of the problem: I have a time series of the (z-)positions of a particle relative to a surface. For 5 independent subsamples of this time series, I calculate the ...
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Interpreting LR test of model fit when additional variables are insignificant?

Suppose we estimate the following (made up) model: $$\tag{1} pizza = \beta_0 + \beta_1 price + \epsilon $$ where pizza is quantity of pizza purchased price is the price of a pizza Now suppose we ...
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How can I derive goodness-of-fit measures (R-squared and chi-square values) from multinom (multinomial logistic regression) in R?

I am running multinomial logistic regression using multinom command in R. However, I could not figure out how to derive R-squared and chi-squared values from it. I somewhat approached my own way to ...
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Deviance as a measure of fit

I have a general question about using deviance as a measure of fit in generalized linear models (i.e. multinomial, poisson etc.). I think I've gotten lost in all the equations and have totally missed ...
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Are most fit indices inappropriate for EFA (not CFA)?

Is it the case that many of the available fit indices generated by package "psych" in R are not appropriate for EFA, only for CFA (even though generated by package 'psych' in R for EFA) not useful ...
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Goodness of fit for multivariate Gaussian with identity covariance

My assumptions: I have $X_1, \dots, X_n, T_1, \dots, T_n \overset{i.i.d.}{\sim} \mathcal{D} , X_1 \in \mathbb{R}^n$. I made some assumptions and have fitted an $f : \mathbb{R}^n \to \mathbb{R}^n$ ...
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Panel Data (Longitudinal) Analysis with SEM with continuous variables

I am estimating a SEM MIMIC model with 2 indicators, and 5 causes of a latent variable. I have a panel of around 170 countries for the period 1960-2018. However, my chi-sq and general fit stats are ...
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Goodness of fit measure for GMM similar to the likelihood function

Suppose we have two trained models for a specific color in an image: 1-Multivariate Gaussian Model (MVG), 2-Gaussian Mixture (GMM). I need to identify the most probable region which then be used for ...
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What fitness test to use if the actual data and expected data has a lot of zeros?

I am testing the agreement of two sets of data with each other, albit testing for the goodness-of-fit. However, both experimental data and model data has actually a lot of zeros in it so chi-squared ...
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Hurdle model “goodness of fit” statistics?

I apologise in advance if this sounds like a stupid question. I am used to GLM with continuous data. I've run a hurdle model in R (pscl:hurdle) with a negative binomial distribution for the "count" ...
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How to improve the fit for a GLM model?

I am fitting a glm model to examine associations between some predictors and a 3-levels outcome variable (see data below): ...
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Assessing goodness of fit for stochastic models

I'm working with rainfall data and trying to construct a stochastic model that models the data well (e.g. seasonality, dry and wet periods, duration of storms, etc.). Specifically, I'm looking at ...
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What is the figure of merite of a *likelihood* fit?

There are two main types of fit to obtain some floated parameters of a model (functional form) on a given dataset : (i) the $\chi^2$ fit, which minimize the $\chi^2$ ii) the maximum likelihood fit, ...

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