# 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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### SEM: High SRMR in model with binary predictor. Other fit indices OK [closed]

In this post I may display severe lack of understanding in SEM and the math behind it so please be kind. I am testing the following structural model with lavaan using MLM (due to non-normality) with ...
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### How to choose and perform a goodness-of-fit test?

I notice there are a lot of questions on the topic (most are along the lines of: how to do a Chi-squared goodness-of-fit test), but mine is perhaps more general. Using an example I recently ...
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### How do I get the sample mean and standard deviation? [duplicate]

I am trying to get the mean and standard deviation for the following sample means with the given sample frequencies for each mean. So in a histogram, the x-axis will show the mean range and sample ...
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### Degree of freedom of different distributions: Chi-Square Goodness of Fit Test

I try to understand why the number of constraints differ for the distributions in the table below, for the Chi-square goodness of fit test. I found the content in the following link. https://www....
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### Over “specification” of a statistics model?

For a simple example, I am fitting data with a likelihood function generated by a normal distribution. The first model is the normal distribution with two-parameters. The second competing model is the ...
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### Anderson-Darling test Critical Values for Log Logistic (asymptotically using Monte Carlo Sim)

I am trying to to compute the AD test critical values for a Log Logistic distribution (not a normality test, but an EDF) . I am trying to do a Monte Carlo simulation in R. The steps are the following:...
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### Goodness of fit ranking for several models

I have some data that I am trying to fit with different models: exponential, sum of two exponentials, hyperbolic secant, etc. I would like to have a criteria to be able to rank the different models ...
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### Goodness of fit for Copula

I was wondering if the graphical methods can be used instead of formal tests such as Cramer-Von Mises test as the GOF for copulas? The scatter plot of pseudo-observations is as follows: The Q-Q ...
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### Goodness of Fit Test vs Testing RMSE

I have a bit of a broad question. It seems to be that there are two different approaches (Borrowing a bit of Breiman's Two Culture's paper) when it comes to testing if our data looks like our model. ...
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### Non-significant result in CFA model

I've fitted a one-factor model to data originating from a unidimensional 8-item scale; sample size is 400. Because the scale uses a Likert response format, and data does not follow a multivariate ...
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### ERGM with larger log-likelihood but worse fit than reference model?

I'm using the R package statnet to fit some ERGMs to the Faux Dixon High simulated network data provided with the package. The first model I fit is almost identical ...
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### How to assess the quality and goodness of fit of a lasso model?

So far I evaluate the lasso model by its out-of-sample predictions and by the $R^2$ for the goodness of fit. What other measures should I look at? Particularly, do I need to examine the residuals for ...
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### Different loss functions for estimation and cross-validation

Assume that the goal is to estimate some parameter $\theta$ (finite or infinite dimensional) based on some data available. Also, assume that there are other nuisance parameters are present in the ...
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### Fish counts and Poisson [closed]

I am having troubles with fitting a Poisson distribution to my data, let me explain: I have fish counts of different species from a closed list, at 5 sites, 2 different depths, and across 10 years. ...
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### Does the large number of sample is the reason for low p-value in GOF test of Copula? (Cramer_Von mises)

I would like to determine a suitable copula function on my data. The multivariate computed from the original data is similar to the Plackett. The GOF test on my data with size 8000, reject all ...
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### Posterior Predictive Check for Hierarchical Logistic Regression Model

I need to apply Posterior Predictive Check (PPC) on Hierarchical Logistic Regression Model (so I have binary outcome) to validate my model (to see goodness of fit of my model). I know that I need to ...
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### Limitations of Kolmogorov–Smirnov test

In this article, it is said that the test statistic tends to be more sensitive near the center of the distribution than at the tails. Can some please explain this what it means? (with a simple example ...
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### Why do I get different results of goodness of fit test using AD tests from different R libraries?

I am trying to find the best method for goodness of fit while testing my data with different models of distributions. I need to use AD test. So I have compared results using two different ...
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### p-value fitting a model to data

I have performed a physical experiment with few (~20) measurements, which have different uncertainties on the y-axis. The measurements were fitted to an exponential model $f(x)=ae^{-bx}+c$ using scipy....
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### How to derive the formula for coefficient (slope) of a simple linear regression line? [duplicate]

There is a formula for calculating slope (Regression coefficient), b1, for the following regression line: y= b0 + b1 xi + ei (alternatively y'(predicted)=b0 + b1 * x); which is b1=(∑(xi-Ẋ) * (yi-...
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### IRT degrees of freedom of item fit statistics

I'm fitting Rasch models with the mirt package. Upon measuring item-wise $Q_1$ using mirt::itemfit(model, fit_stats="X2"), I ...
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### ugarchfit diagnostic tests: goodness of fit

I modeled a couple of financial return time series with different kinds of GARCH-models and different distribution termns and now whant to compare them. I very often face the problem that all ...
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### Why Lack of fit test is significant?

I fitted a dose-response curve and part of my data is significant for Lack-of-Fit test, but I don't understand why? If visually the model has a good adjustment. I know the Lack-of-Fit test is not a ...
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### How to confirm more people selected “Agree” than is possible by chance [closed]

In the table below, how do I prove statistically that more people are in the group: "Sum of Agree", than is possible by chance? I do not know which test to use here, (although I am using the Extended ...
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### I would like to find Goodness-of-fit between my differential equation simulation result and observed field data. How to find it?

I modelled a ecological system using ordinary differential equation. Simulated the model for 12 months. I also have 12 months of field data. Now I want to find the goodness of fit between my model ...
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### Including probabilistic information in the model fit assessment of multivariate nominal regression

I have a ground truth nominal variable $Y$ and a continuous predictor variable $X$. I have split these up into a training dataset, $Y_1$ and $X_1$, and a testing dataset, $Y_2$ and $X_2$. I want to ...
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### Data generation under Pitman alternatives

I would like to numerically simulate the power function of the goodness-of-fit test $T_n$ in https://projecteuclid.org/download/pdf_1/euclid.aos/1176348133 for a set of certain probability ...
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### Is it possible to define an optimal fit?

Let assume that we have n pairs of real numbers: (x_1, y_1), (x_2, y_2), ..., (x_n, y_n) Let as also assume that ...