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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Interpreting and reporting CFA results (localized areas of ill fit indicated by MI)

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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24 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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66 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 ...
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42 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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23 views

goodness of fit test: kolmogrov-smirnov

it seems that lognormal and burr distributions are the best to fit my data. Can I compare there goodness of fit using Kolmogrov-smirnov test? Lognormal has 2 prameters where Burr has 3. That's why I'm ...
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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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18 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
29 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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19 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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41 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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110 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
123 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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20 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
35 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
80 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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38 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
61 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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24 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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21 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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93 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 ...
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39 views

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 models?
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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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43 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
36 views

$R^2$ 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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39 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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28 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 ...
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1answer
47 views

Compare model fit for model trained on different data

I have two datasets, where I'm predicting y from x using a basic linear model for each dataset. Both models are significant, but ...
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14 views

Is there a goodness of fit test for Poisson regression with complex survey data?

I am doing an analysis of complex survey data using a binary response variable and several covariates. I am using Poisson with robust standard errors to obtain relative risks. Is there an ...
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Is it safe to assume that $\ln{L} = -\frac{\chi^2}{2}$?

I have written a code that fits a 2D model image to some observed 2D image. One of the optimization libraries I use (MultiNest) in order to do that requires to be ...
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Chi post-hoc OR Z cell comparisons: do 2 proportion z-tests indicate most significant factors?

Attached is an example of some data I'm working with. I'm testing the occurrence of a rare behavior, while controlling for both education and the "bin" variable. The observed sample size is 129. This ...
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Goodness-of-fit tests for logistic regression

from my knowledge, there are two approaches to evaluating whether the model fits the data in logistic regression. First is the predictive power. Second is from using goodness-of-fit tests. My ...
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Interpret 2 columns of p-value in Pearson's goodness-of-fit test

In author's materials, he said that under the null of a correct distribution, the asymtotic distribution of P(g) is bounded between Chi-square(r-1) and Chi-square(r-k-1) where k=# estimated ...
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Elastic net regression's goodness of fit

I have a (possibly stupid) question about interpreting my elastic net regression model. My response variable is continuous and I have 32 variables (some are correlated) as the predictors (for 53 ...
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1answer
91 views

A non-uniform distribution of $p$-values…again

There appear to be many multiple-hypothesis-testing situations that result in a non-uniform distribution of $p$-values. I would like to describe one simple numerical experiment, and understand why it ...
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implications of poor model fit in survival analysis

Can a survival analysis model with poor model fit still be useful in reporting? I have set up a time-varying survival analysis model (Cox regression in SAS), and have found it to have poor model fit. ...
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Chi goodness of fit to check how many values fall in bins

I have a lot of data about occurrences of hashtags. I have already checked if the occurrences follow a power law distribution (estimating parameters with MLE from data). Moreover I've estimated the ...
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28 views

Does the theory fit the given data?

We are given that the members of a community are classified by blood type according to the following schema: \begin{array}{|c|c|c|c|c|} \hline O& A & B & AB & Total \\ \hline 121 ...
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Characterizing hour-to-hour differences and against a mean

Assume that I have a dataset that shows the number of foosball games that a trainee has played per hour in an 8-hour day of practice (assume games are brief and there is no limit to the number one can ...
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Goodness-of-fit test

I have a question regarding goodness-of-fit tests. A general rule of thumb with the chi-square test of goodness of fit is that (1) no more than 20% of your expected frequencies can be less than five, ...
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How to measure the goodness of fit of a 3D line?

I have data points in 3D space, and I'd like to quantify how well they conform to a straight line. Specifically, this is a body tracking problem. I have multiple options available for the 3D ...
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Assessing fit of the CFA model with polytomous indicators (the graded response model)

I fit a graded response model using R package lavaan using function cfa. This function fits ...
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33 views

Goodness-of-fit for Discrete Distributions

I've been doing some data analysis with Scipy. So far I accomplished this with continuous distributions: I can fit a probability distribution to a set of data points using a maximum likelihood fit. ...