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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Can I compare chi-square values for goodness of fit tests to see which observed distribution deviated most from its null distribution?

I have a series of goodness-of-fit tests using chi-square a few of which are below, $$ \begin{array}{r|r|c} \text{df} & \chi^2 & \text{Reject } H_0 \\ \hline 49 & 1744.68 & \text{Yes}...
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Poisson regression modelling using PROC GENMOD – impact of grouping on fit statistics

I am trying to model claim rates using poisson regression. Please find example SAS code below: c is the number of claims, n is the number of insured vehicles, car and age are categorical properties of ...
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14 views

Fit parametric distribution to time-series data

I have a time-series of daily revenue data for a number of years and I would like to perform a parametric distribution fit to the data. Given that distribution fitting requires i.i.d. data, I presume ...
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37 views

How to measure goodness of fit for a poisson regression model?

I am working on a poisson regression model in sas. But I am not able to determine how good the fit is. I have used PROC GENMOD, PROC NLMIXED, PROC GLIMMIX and now I want to compare the results. How ...
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982 views

Overfitting: No silver bullet?

My understanding is that even when following proper cross validation and model selection procedures, overfitting will happen if one searches for a model hard enough, unless one imposes restrictions on ...
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0answers
29 views

Hosmer-Lemeshow test in R

The Hosmer-Lemeshow test is a statistical test for goodness of fit for logistic regression models. According to ?hoslem.test, it deals only with binary logistic ...
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17 views

Rsquared / R2 (i.e. R²) for Gamma-GLMM?

I have successfully calculated R²c as a goodness-of-fit measure for GLMM's using the r.squaredGLMM function implemented in R's <...
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10 views

Binary outcomes with low goodness of fit (GOF) but good predictive power?

We know that it is possible that a model predicts the outcome reasonably well (and hence high R-square) but is actually misspecified (and hence low goodness of fit), as this example shows. The ...
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7 views

Goodness of fit (R-squared) for SUR

I would like to compare the goodness of fits statistics, $R^2$, of different statistical models estimated by the seemingly unrelated regressions model. In the lecture note of Professor Thorton on SUR,...
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18 views

How to propagate “model covariance” into a covariance matrix?

I have a theory $f$ (actually a set of coupled non-linear differential equations) that, from a vector of $n$ initial conditions $\vec x$, is able to predict $m$ values $f(\vec x) = \vec y$. I can ...
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7 views

Goodness of fit test for discrete distributions from mean and variance only

What is the best way to perform a goodness to fit test for two discrete univariate distributions knowing only their mean and variance? I don't know the nature of these distributions and I was only ...
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2answers
178 views

How to evaluate how well some samples come from some given distributions?

I have a complicated procedure that, given an input $x$, outputs several random samples $S_i(x)$ for $i\in\{1,\dots,k\}$ (each sample consists of $n_i$ points). Each sample $S_i(x)$ follows an unknown ...
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1answer
15 views

Fitting and comparing distributions based on diverse summary statistics

I have a bunch of samples, about 35, drawn from a fat-tailed distribution. I think it is reasonable to assume that the samples are all drawn from distributions from the same distributional family, ...
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1answer
26 views

n/m asymptotics and logistic regression goodness of fit tests

in the case of logistic regression, say our model has $p$ covariates and we have $J$ distinct covariate patterns (distinct combinations of the values of the p covariates) and we have a total of $n$ ...
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1answer
27 views

What does excessive correlated residuals (as indicated by modification index) say about a model?

This question/post is a follow-up to a few previous posts so please forgive the redundancy. My question is what excessive number of modification indices suggesting high number of correlated errors ...
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1answer
35 views

Reporting focal strain (high MI) for CFA models with good model fit?

According to Brown (2015), one is expected to examine and report localized areas of ill fit (e.g. modification indices (MI)) as part of the model evaluation. I have a number of questions about ...
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27 views

How to determine if a set of data is Student-t distributed

So I know how to use goodness of fit tests generally. For example if I wanted to check whether my data came from a Poisson distribution I would first estimate the parameter using MLE (so just the ...
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1answer
101 views

How freqently are the information conditons for proper Akaike information criterion application actually met?

Akaike information criterion (AIC) is limited to goodness-of-fit for assumed distributions. That is, for an assumed distribution (especially homoscedastic) one can assume a maximum likelihood function....
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1answer
47 views

Why does Bayesian p-value involve the parameters in addition to the data?

On page 146 of Gelman's Bayesian Data Analysis, Gelman discusses Bayesian p-value as a way to check the fit of the model. The idea is to compare the observed data ($y$) with data that could have been ...
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1answer
48 views

Can I compare goodness of fit using the Kolmogrov-Smirnov test, if the distributions have a different number of parameters?

It seems that lognormal and Burr distributions are the best to fit my data. Can I compare their goodness of fit using a Kolmogorov-Smirnov test? The lognormal has 2 parameters whereas Burr has 3. To ...
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10 views

Goodness of fit for complex valued curves (i.e. frequency responses in frequency domain)

I'm not a hero at statistics, som my apologies for perhaps the stupidity of this question. Presume that one has the frequency response $Y_{data}(k)$ and also has the synthesized response $Y_{syn}(k)$. ...
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1answer
18 views

Selecting the best SEM model based on goodness-of-fit statistics and number of observable variables?

I am a PhD student in the field of economics. As part of my research work I am setting a SEM model. I have designed two models that present acceptable goodness-of-fit statistics respectively. ...
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22 views

Distinguishing between Poisson distribution and a similar distribution w/ small mean

I have an experiment where if all is going well the measured distribution should be Poisson (to very good approximation) with mean $\lambda \sim .1$, but if something goes wrong the distribution will ...
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2answers
31 views

How to determine the similarity between histograms

The questions is asked at How to assess the similarity of two histograms? However, I'm not sure if it's the same question as mine, so I'd like to ask again. I have a dataset, which covers a long ...
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27 views

Evaluating hetroskedasticity in a binomial residuals vs. fitted plot in glmer?

I am trying to validate the goodness of fit of a model in glmer using residuals plotting. I went through many threads here related to this but still I am not sure that the solutions offered apply to ...
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48 views

Feature selection and model fitness in panel data

I am interested in panel data analysis with more than 20 variables in R using the package "plm". Right now, I am looking at adjusted R-square for the set of variables that best explain my dependent ...
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113 views

Am I calculating the Anderson-Darling statistic correctly for comparing PDFs?

I want to compute the Anderson-Darling statistic to use as a goodness of fit test for some PDF distributions. I am using R. I want to compare some models to the observations, which are my baseline. ...
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3answers
127 views

Goodness of fit test on sparse contigency tables with high dimensionality

I have a vector of size 1x3500, which can be viewed as the 'known distribution'. It is simply a table of counts across 3500 groups (i.e. a contingency table). I also have $N$ other vectors of the same ...
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10 views

“Goodness for fit Chi” test on point pattern

Apologies, I have a few question today I hope there is no limit to how much I can ask here before you start billing me :) What is the meaning of Goodness for fit Chi-sqaure test? From the wikipedia ...
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7 views

How to evaluate the quality of Bayesian network sampling?

I have generated a sample from a Bayesian network by applying Forward Sampling. I learn the parameters of the network (the same structure) from this sample so as to evaluate the quality of the sample (...
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25 views

Scaled vs. unscaled Chi-square statistic in CFA / GRM fit evaluation

I generally want to assess the fit of a CFA model with ordered categorical indicators (the graded response model, GRM). There are two versions of this model, the normal-ogive GRM (ordered CFA with ...
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1answer
36 views

chi-squared test of two row table while calculate cells in row 2 from total n of row 1- is this valid to do?

I have count-data of patients with an event which occurred on different days in the week. For example: ...
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1answer
84 views

Test goodness of fit for geometric distribution

Consider a set of variable length non-overlapping intervals on a discrete finite number line. ...
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1answer
19 views

Justification by enhancement of $R^2$

Is (great) enhancement of $R^2$ sufficient to justify the use of another model ? other desciptives variables ?
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42 views

Chi-squared goodness-of-fit test and conditional probability distribution

I have three discrete variables, let's say $A, B,$ and $C$. The number of possible values of $A$ is 3, and $B$ and $C$ take binary values. I also know the probability distributions, $Pr(A | B, C)$, $...
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1answer
64 views

How to make a model for the given data in sas?

I have a nonlinear model: $$r10^{\beta_0-\beta_1A-\beta_2B-\beta_4D-\beta_{2,4}BD} $$. I used sas to test different models. Here is the code: ...
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26 views

Power Law Fit goodness of fit test

I've been reading the paper by Clauset et al. on fitting power laws. However, with the amount of data I have the p value test they propose will not work. They suggest creating 2,500 fake data sets, ...
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1answer
24 views

How to check model adequacy in Poisson regression?

My data contain positive integer valued response and so I want to use Poisson regression. But I am unable to interpret the output given by glm().
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Terminology: Can “goodness-of-fit statistics” and “indicators” be used interchangeably?

I want to use several indicators to determine the goodness of fit of my model, such as R square, K-S, chi-square etc. What should I call them? Can I call them goodness-of-fit indicators? I see a ...
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35 views

Goodness of fit with 1000 or more observations

When we have a lot of observations (for example 1000), and we want to find a "valid" distribution, which test should we perform ? Or how should we do ? Why the number of observations is important ? ...
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111 views

Fitting negative binomial distribution to large count data

I have a ~1 million data points. Here is the link to file data.txt Each of them can take a value between 0 to 145. It's a discrete dataset. Below is the histogram of dataset. On x-axis is the count (0-...
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Deviance vs Gini coefficient in GLM

What are the pros and cons of using Deviance as opposed to Gini coefficient when measuring the quality of regression / classification models? From experience, I see that people like Gini more than ...
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Goodness of Fit and reliability of coefficients in Logistic Regression

I have logistic regression model with 9 independent variables. Two of them are numerical, the others are binary. Three of my coefficients are significant at 0.001, two of them are significant at 0.05. ...
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I need help to determine the distribution

So I have an assignment to estimate the distribution of different sets of and then make a goodfit test to see if the assumption is correct. This is my current histogram, and I have tried both ...
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If the conditional expectation of the random variable does follow a linear function, can we show the probability a particular data set happens?

Suppose that $\mathbb{E}[Y\mid X=x]=\beta_0+\beta_1x$ where $X, Y$ are random varibles. Given a set of observations consisting pairs of $X,Y$, is it possible to attach it as probabiltiy density ...
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59 views

Measure of “deviance” for zero-inflated Poisson or zero-inflated negative binomial?

Scaled deviance, defined as D = 2 * (log-likelihood of saturated model minus log-likelihood of fitted model), is often used as a measure of goodness-of-fit in GLM models. Percent deviance explained, ...
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1answer
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$R^2$ in a model with no intercept is $R^2_u$, the uncentered $R^2$?

From Hayashi, 2000, p.20, I've understood that we can have some troubles in computing $R^2$ when the constant is not included in our model (e.g. negative $R^2$), but we can avoid them using $R^2_u = \...
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52 views

Goodness of fit of vector error correction model (VECM)

I am trying to find the relationship between S&P and six macroeconomic variables using vector error correction model (VECM). What are the criteria for assessing the overall performance of the ...
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33 views

Using AICc distributions to assess goodness-of-fit and model selection

I have a couple of ordinary differential equation models that I'm trying to fit to time-dependent biological data ($y_n$). One model is more complex than then other as it has more free parameters. I ...