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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Measuring goodness of fit/is chi-squared appropriate?

I'm a physics rather than statistics student so please bear with me... I've got a simulation which produces some deterministic curves of the area covered by a particular weather system over time. ...
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What features can be extracted from a probability distribution? [closed]

I have been looking online regarding feature extraction and I am looking at extracting features from probability distribution by getting the characteristics of the distribution. I know that most ...
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what is a good measure of goodness of fit for survival models that can be used for comparison between models?

I don't see any of such measure in the output from coxph() in R (Cox proportional Hazard model). Is there a goodness of fit measure for survival models similar to R2 for linear regression? Update: ...
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Test goodness of fit of a multivariate distribution via testing GOF of linear combinations of components

I am modeling a continuous bivariate distribution of a random vector $(X_1,X_2)$ using a copula. I would like to assess how well I am doing. Given a data sample, I could probably do a bivariate ...
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How to calculate the sample cumulative distribution function for a Kolmogrov-Simulation test to examine the goodness of fit with given data?

I have sample data for 'Times between successive crashes of a computer system' which is for a 6 month period and the data is given in hours. The data in brief is : 1,10,20,30,40,52..... I need to use ...
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Cox-Snell residuals from Cox model in R (cch-function)

I am working with a weighted Cox regression model created using the cch-function from the survival package in R: ...
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negative values for AIC and BIC

I am trying to fit a gumbel distribution using MLE for the following 10 data points. DATA=(3.62,3.76,3.57,3.56,3.61,3.77,3.46,3.6,3.39,3.74) The problem is that the ...
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Goodness of fit for logistic regression with ONLY categorical predictors

I performed a logistic regression with ONLY categorical predictors. It has goodness of fit statistics as below. The Deviance and Pearson Chi-square look bad, but other measurements and ROC look fine. ...
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Goodness of fit for LPM

I want to carry out goodness of fit statistics for a Lineary Probability Model. However, given that R^2 might not be the best choice, I am wondering which other options would be worth looking into?
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How to assess GEE quality and fit, e.g. by residuals(?)

In contrast for generalized linear models (for GLM, there is e.g. AIC and null vs. residual deviance), I could not find such criteria implemented in R to judge my generalized equation (GEE) models. Is ...
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What do you mean by a model is adequate?

I'm learning about regression and stumbled upon this part where we check the accuracy of the model. In order to do that, we do an F test with the null hypothesis stating that the model equation is ...
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Is linear regression appropriate here? Number of points within district based on racial proportion of that district

Each map district below is shaded blue according to the percentage of its white population. The colored points are healthcare facilities. I want to determine whether or not to reject the null ...
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Joint asymptotic distribution and measures of fit

I have been looking for something similar but couldn't find any, unfortunately. Some help would be much appreciated. Consider a simple bivariate linear mean regression $$y=\beta x + e$$ where $E[e|x]=...
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Difference between Chi^2, Chi^2/dof and R^2

I have radioactive decay experiment (so the model is y = Ae^(-kt)) results and am (slowly) teaching myself mathematica to plot this. I want to output some measure for the goodness of fit, but am ...
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Is the percentual of deviance explained the same as the Mc Fadden's Pseudo R2 in glm?

I want to calculate the percentage of deviance explained for my glm model. I read in some comments that McFadden is the same as % of deviance explained only when ...
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Chi-Square Value too small for df = 6, am I using the wrong number of df?

I'm not very good at statistics so I figured I could ask here to see if anyone could help me. I need to do a goodness of fit test for a table of 7 data points: Energy Observed Flux Expected Flux 0.3 ...
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Goodness-of-fit for discrete distribution - tails issues

In general, I want to see if a set of values comes from a certain discrete distribution (in this case integers from Poisson, or maybe gamma-Poisson). Chi-squared consistently comes up as the best GOF ...
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How to account for measurement error when computing explained variance

Let's say that I am fitting a linear regression model to predict random variable $Y$ based on random variable $X$, and I know as a fact that the only random variable that detemines the value of $Y$ is ...
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A very big JB value in Jarque-Bera test [duplicate]

I have run the JB test for my data using two different commands. I am quite clueless about what conclusion I can make from the second picture which shows results of 0. This tells me that there is no ...
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Chi Squared Fit Statistic in Structural Equation Models

I am interested in structural equation modeling. I am trying to get to the bottom of how $\chi^2$ is calculated for a structural equation model. I understand that outside of structural equation ...
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Appropriate exponential goodness of fit test for unknown parameter

I have a set of univariate data (n=1000) that I believe to be exponentially distributed. I also have a separate, but inexact, prior estimation for the mean or parameter of the distribution I expect ...
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Quantitatively, how powerful is Shapiro-Wilk or other distribution-fit tests for small sample sizes?

I'm looking for an analysis (I assume a book or website, but feel free to put it all in comments here) that provides an in-depth discussion of the power/accuracy of normality assessments such as ...
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Evaluating/defining CDF on a hypersphere/hypercube [closed]

I have a set of data defined on the positive orthant of the hypercube. I can project that data onto the positive orthant of the hypersphere, or the simplex. I can then assign a distribution to that ...
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Which of two parameters was chosen for a sample?

Problem: $X$ is chosen to be $\text{Geom}(p_1)$ with probability $\frac{1}{2}$ and is otherwise chosen to be $\text{Geom}(p_2)$. Given a sample of size $n$ from $X$, guess whether $p_1$ or $p_2$ was ...
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Pseudo R squared for the negative binomial regression

I am confused with the Pseudo $R^2$ computation of the negative binomial regression model. For the logistic regression, we can compute the Pseudo $R^2$ as ...
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Scale invariant goodness of fit for one model's fit across multiple datasets

Suppose I have one model, and (in my case) tens of thousands of datasets. I'm interested in scoring how well this one model fits across all datasets, and the comparison is more to identify a subset of ...
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Goodness of fit for a multi-level model

I'm currently trying to figure out how to properly express a 'goodness of fit' criteria for a Bayesian model that has several steps. I have a 2 dimension dataset of position values (x and y) and ...
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Is Chi Square test statistic too large to draw conclusions?

I collected some data regarding purchase behaviour (purchasing a black or white car), before and after updating the background color of an e-commerce website. I would like to know if the change was ...
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Comparing fits of linear models that use different data spans of a curve (and why does AIC seem to work)

Several related questions have been asked. This one is similar, but it does not match this question exactly. Also, i seem to have results that contradict the accepted answer there. Data An imperfect ...
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Goodness of fit for heavyLme

I was analyzing repeated measures data with linear mixed models with the lmer function, but due to heavy tailed residuals (image below) I am now using the heavyLme function. I wanted to compare the ...
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Fit the best distribution on different samples

I have 10 vectors of counts of particular events. For example, in Vec A each event is the count of times I sample a ball of a particular color. For Vec B it's the count of word frequency in a ...
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interpreting pearson chi-square

I ran a Mackenzie Bailey goodness of fit test on a model that fit data with 26 surveys and 46 sites. There were 4 categorical covariates included. The pearson chi square value is large, and the ...
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Likelihood ratio test for Markov orders - What succession of tests?

I want to estimate the Markov order of a binary sequence. For that I calculated transition matrices and the log likelihoods for the orders of interest 0,1,2 and 3. Essentially the one with the highest ...
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Checking Conway-Maxwell-Poisson model adequacy

I am trying to troubleshoot model adequacy problems for underdispersed count data (number of correct responses in a simple task; dispersion ratio is 0.3) that I modeled with Conway-Maxwell-Poisson. ...
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Evaluate the quality of the negative binomial regression model fit

Our response variable is highly skewed and there is evidence of overdispersion as well. We tried with the Poisson, and Quasi-Poisson models. Both Poisson and Quasi-Poisson models failed to satisfy ...
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Goodness-of-fit test for conditional distribution

The chi-square goodness-of-fit test allows us to test if a data sample $(y_n)_{n=1,\ldots,N}$ agrees with some proposed model distribution $P(y)$. However, in a typical machine learning setting we ...
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Appropriate goodness-of-fit test for the negative binomial regression

I have used the following Pearson $χ2$ test and the deviance test to assess the negative binomial regression using R as ######################################### ...
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Best practice for establishing configural invariance?

I was hoping for some perspectives on the best practices for establishing configural invariance using ordered indicators with WLSMV estimation. I have a 3-factor scale and I am assessing invariance ...
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Reduced chi-squared for models fit to different subsets of data

I have some data to which I am fitting piecewise linear models. I want to select different subsets of the data, fit a model to each of them, and then compare which subsets are best able to be ...
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Which goodness of fit test to use?

I have two different vectors and I would like to compare these with each other so I could say that statistically the distributions come from the same sample. The data is below: X1: 149 144 140 135 131 ...
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goodness of fit for psychometric data (perceptual threshold)

I'm running an experiment on perceptual thresholds in audio. I'll try not to bog you down with too many details: The experiment is about vibrato speed; specifically, when can you tell the difference ...
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34 views

goodness of fit test to check for normality

I have task about hearing ability and here is frequency table bad ability average good ability total 19 64 17 100 It is said that average ability is everything +/- 1sd. This is all data I have. I ...
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Is there a G-test equivalent for continuous variables?

The G-test is similar to the chi-square test for goodness of fit. It is proportional to the kl-divergence. I am wondering if there is a similar test that is applicable to continuous variables. Since ...
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Calculating the tail bounds for a beta-binomial regression

I have a beta-binomial regression model that depends on a probability $p$ and a given over-dispersion $\beta$ and is used to parametrise the distribution of $Y$ in the following way $$ Y(x) \sim ...
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How to select and interpret Goodness of fit test for an epidemiological study with small sample size?

I have a study that found an association between exposure to antidepressants and the risk of preeclampsia. The number of women who were exposed and had an outcome (i.e. preeclampsia) was small: 10 ...
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Joint estimation of OLS and Logistic Model

I ran two equations for panel data, the Q (OLS model), the second is ERM (Logistic model), the main independent variable in equation 1 is the main dependent var in equation 2. To solve the endogeneity ...
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Compute sigma significance from chi2 goodness of fit

Let's assume I have some binned data, which I have fitted with two curves (two hypotheses). Each fit yields a different chi^2 value and degrees of freedom, such that I can already see clearly that one ...
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How do I calculate effect size for Anderson-Darling test?

I'm looking at the list of tests and effect sizes on https://cran.r-project.org/web/packages/statsExpressions/vignettes/stats_details.html, but I can find any way to calculate effect size for Anderson-...
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Goodness of fits tests. Multiple sample test

I have a question. Please help me: Assume we need to test at a particular level (say, 10%) whether clients are equally likely to complain about quality of service at three firm branches. In the ...
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Improving fit of underdispered beta regression model in glmmtmb

I have survey data where the outcome is the proportion of a research budget interviewees wished to assign to one of three different "types" of research into solutions for various issues. I ...

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