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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55 views

Unbiased estimator for $L^2$ probability distance norm

I am trying to find an unbiased estimator for (what looks like) the $L^2$ Wasserstein distance between two probability measures. I'm pretty sure that by bickel-lehmann, there is an unbiased estimator. ...
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2answers
466 views

Significance vs. goodness-of-fit in regression

Assume that I am interested in analyzing the following linear regression model: $$ Y = \beta_0 +\beta_1 x_1 +\beta_2 x_2+e $$ Please explain the difference between testing the p-value for each ...
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119 views

What is the difference between Shapiro-Francia and Shapiro-Wilk tests of normality?

I apologize for this easy/basic question. Please forgive me if this is a duplicate question. I've been researching the Shapiro-Wilk test (1965) of normality for a project. In doing so, I found an ...
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247 views

Is the covariance matrix a diagonal matrix with variances on the diagonals?

I am a geophysicist learning about geophysical inverse problems. In many papers, the authors discuss the "covariance matrix" as it applies to the inverse problem. In most geophysical applications, ...
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34 views

Finding a distribution that fits different observations of data

I am observing session lengths on a network. I want to fit a distribution to the data that I have collected. I have data from two different observations (about a month apart). The plot below shows ...
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1answer
753 views

Fit Hawkes process to 1d data using python package TICK

How can one fit the 1-dimensional Hawkes process with exponential kernel to the experimental 1d dataset (t1,t2,t3...tn) and check the goodness-of-fit via tick python3 package? I found on official ...
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90 views

Evaluate Bayesian SEM goodness of fit blavaan

I'm currently trying to identify how to evaluate model fit with Bayesian SEM. I've been reading that the posterior predictive p-value can be used, with a p-value of approximately 0.5 indicating good ...
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31 views

Inference using model with low goodness of fit.

Assuming a model is correctly specified, would it be appropriate to draw inferences based on a model with a low Goodness of Fit (~0.15)? Of course, using such a model to make predictions is likely ...
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4answers
1k views

Linear regression with negative estimated value for intercept

Does a negative value of intercept suggest that the regression line provides poor fit to the data? why? and why not?
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1answer
114 views

Goodness of fit test

What is the intuition behind pooling frequencies that are less than five in a Chi-squared goodness of fit test? Even though I have been told that it is not used in industries today, the concept is ...
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1answer
19 views

Chi2/ANOVA testing on sets of much different size

I am trying to decide on which stats test to use to determine if the number of males/females is higher on people who decided to buy a product versus those who didn't buy a product. 96000 people didn'...
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97 views

Model Selection: Goodness-of-Fit Statistic when Noise is Unknown (vs Reduced Chi-Squared)

I have data D_k and different models M_i, and I would like to calculate a goodness-of-fit statistic for undertaking model comparison between the different M_i's, in the case of unknown uncertainties ...
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372 views

Residual plot for panel data question

Currently, I am doing a panel data analysis to predict/forecast the housing prices, and I want to use a residual plot to detect if my model is ok or not. I have been reading many articles showing how ...
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What are the pros and cons of different metrics for evaluating a logistic regression model?

In the data science world, I have always evaluated the performance of logistic regression models simply using ROC/AUC. However recently, I've read from some traditional statistics source about some ...
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1answer
198 views

Why don't I see my points on Cullen and Frey graph?

I have a set of data of 5 members. based on some previous questions , I was expecting to see where my actual points are located on the graph. in my case I see the theoretical but not my points. just ...
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1answer
42 views

Test which one of two (mechanistic / non-regression) models fits the observations better

There's a large number of similar questions, but they mostly seem to be about regression models and deal with cross validation, comparison of nested statistical models via likelihood-ratio, etc. ...
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53 views

Goodness of fit test for observed samples of binary strings

Consider a process that produces binary strings of varying length $n$. A typical sample would include $n\ $ I Number of strings $1\ $ I $\ 3,000,000$ $2\ $ I $\ 800,000$ $3\ $ I $\ 350,...
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57 views

Goodness of fit for weighted regression

Is there a goodness of fit metric similar to R^2 that can be used to evaluate a weighted regression? In my particular case, my data points are cities and I weight a regression of this data by city ...
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20 views

Dau Genton test - in grandmothers terms

tl;dr Can you explain the Dau Genton test in terms a median grandmother could understand? Background: So I am looking for an "in.chull" for multivariate, concave hull, and I was going through "...
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462 views

logistic regression binomial data in python using GLM - interpreting output

I have binomial data and I'm fitting a logistic regression using generalized linear models in python in the following way: ...
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3answers
153 views

How is the statistic $\frac{(Obs-Exp)}{\sqrt{Exp}}$ distributed as standard normal?

When testing deviations from an expected categorical distribution, the statistic $\Sigma\frac{(Obs-Exp)^2}{Exp}$ is commonly used and said that this statistic is distributed as $\chi^2$. From the ...
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1answer
64 views

Goodness of fit for two samples with uneven different sizes

I have 2 different samples and would like to test a hypothesis about some aspect of their distribution. The first sample has 11,000 observations but the second is just 150 outcomes. From graphically ...
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1answer
43 views

To report the fraction of explained variation, should I use R2, adjusted R2, or crossvalidated R2?

I am fitting a linear model (normal error structure) with several linear predictors. In R: lm(y ~ x1 + x2). I need to report how much variation in y my model explains. Which of the following ...
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63 views

What criteria to use for goodness-of-fit test for normal distribution ?

There are several goodness of fit tests, may be chi-squared is most famous one, however it seems it is not a preferable choice to be used in the case of continous variables. There is an excellent ...
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1answer
213 views

Goodness-of-fit test on arbitrary parametric distributions with estimated parameters

There have been many questions regarding this topic already addressed on CV. However, I was still unsure if this question was addressed directly. Is it possible, for any arbitrary parametric ...
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1answer
1k views

Path analysis with perfect fit (RMSEA = 0; df = 4; Chi-Square = 3.972) is that too good to be true?

I created my first path analysis model with lavaan. Despite having a big sample (N = 600) my robust analysis has a perfect fit. I'm a bit suspicicous when something is perfect when I am doing ...
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2answers
445 views

How to compare goodness of fit between different distributions in R?

I have some annual maximum data and I want to fit them with some statistical distributions. Theoretically, annual maximum data can be modeled by a Generalized extreme value distribution (GEV), however,...
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1answer
428 views

How to improve fit of distribution to data

I'm trying to fit one of common expenential distributions to data using histfit. However it seems that results aren't as good as expected - it seems that peak should be higher. Histograms presents ...
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1answer
855 views

Goodness of Fit for Poisson Regression using R

I am trying to determine how well a Poisson model fits my data using Residual Null and Saturated Deviances. The Y col is the # of pennies that landed in a cup and the cup column represents the size. ...
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1answer
104 views

Good Text for Shapiro-Wilk Test

I was wondering if anyone can give me some good texts for understanding the Shapiro-Wilk test. I'm searching for an intermediate level text, not too simple like the wikipedia page (it gives very ...
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1answer
66 views

Fitting a finite mixture: choice of the distribution and model selection for the number of components

This is a question about finite mixture models (FMM). We want to fit a dataset $D$ but we are not 100% sure of which distributions we should use to create the mixture; we do not how many clusters ...
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1answer
126 views

shapiro test for exponentiality [closed]

After running the shapiro.exp.test in testing for exponentiality I am getting powers of the test as equal to zero. I suppose the issue might be on my rejection criteria (i.e ...
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49 views

Test for positional amino acid enrichment

I have a question about which statistical test to use for a particular research question. I am studying protein binding motifs (amino acid sequences that other proteins bind to), typically these ...
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1answer
59 views

Can pseudo $R^2$ be used to describe Fraction of Variance Explained?

I have recently done some Logistic regression analysis whose results I will be presenting to my non-mathematician colleagues. One of the key aspects to this is how well the regression fits the data in ...
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1answer
99 views

Adequacy of logit model with oversampled data

I fitted a binary logit model with unbalanced data which were oversampled using SMOTE. This gave an excellent ROC curve but very poor adequacy - the zero hypothesis of adequacy was rejected by ...
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165 views

Interpreting the best-fit student t distribution (based on maximum likelihood estimation) for my datasets

I have fitted (through maximum likelihood estimation of parameters) a number of leptokurtic probability density functions (i.e. logistic hyperbolic-secant Laplace log-logistic student's t (with ...
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222 views

Is KS test really appropriate when validating a power law/estimating power law parameters?

I'm attempting to find out whether some highly skewed data are drawn from a power law distribution, following the popular paper by Clauset, Shalizi and Newman, 2009. Clauset et al. use the Kolmogorov-...
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299 views

Goodnes of Fit Measure for Heckman Selection Model

I am working with a two-step heckman selection model. In the first step the selection occurs based on a probit model, in the second step the mean equation is fitted with a linear model where the ...
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1answer
804 views

interpretation of deviance in logistic model

In logistic regression model for binary data, If the residual deviance(2*(likelihood of saturated model-likelihood of my model)) is 56.728 with df=117, what can I say about the lack of fit of the ...
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1answer
172 views

How is goodness of fit estimated in SEM models?

Structural equation models allow for estimation of complex networks including latent and observed variables, and endogenous and exogenous factors. When an SEM is fit, the model results are summarized ...
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34 views

Goodness of Fit (weighted least squared) using variance instead of standard deviation

Is goodness of fit measured by weighted least square sometimes done by using the variance instead of the standard deviation in the denominator? What I mean is the following. Lets consider the ...
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337 views

Goodness of fit with parameter estimation for non-normal distributions [closed]

I am looking for library in R which can test a vector for different parametrized distributions together with parameters estimation, which returns Anderson-Darling statistics and p-value. Let’s say ...
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1answer
349 views

Formula for standardized root mean square residual (SRMR) in longitudinal latent variable models (SEM, CFA)

First note, related: What is the formula for Standardized Root Mean Residual (SRMR) in the context of latent variable models (e.g., SEM, CFA)? I was wondering what the adaption to the formula should ...
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23 views

Compare the quality of distribution fits

I have two random variables $A$ and $B$ they are of different size. Both are well fitted as $\gamma$ distributions. My question is to find which one is more gamma like. Could You help me to solve ...
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1answer
112 views

Can I use chi-square to test goodness-of-fit in a generalized least-squares regression?

I am performing a generalized least squares regression based on a design matrix $X$, a response vector $Y$ and a (non-diagonal) covariance matrix $C$, assuming Gaussian errors. I'm not sure what ...
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215 views

binary logistic regression with large sample size [duplicate]

I try to make a binary logistic regression model from 85871 samples. I used enter method. There are seven explanatory variables and all of them have significant in Wald Test. But, in Hosmer Lemeshow ...
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1answer
388 views

Goodness of fit for multivariate gaussian

What are good tests to check if the data is generated by multivariate jointly gaussian distribution. I know $\chi^2$ test is commonly used as a goodness of fit metric but I did not understand how to ...
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0answers
140 views

Estimating model fit in multiple mediator SEM

I'm building a multiple mediation model in lavaan. My research question concerns to what extent a relationship between a continuous X and a binary Y is mediated by two continuous mediators M1 and M2. ...
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569 views

Comparing similarity of two distributions

I'm building a simulation that outputs data in distributions and I need a metric to know how similar they are to ground-truth data. Specifically, I output things like this, which is a distribution of ...
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1answer
80 views

Measuring how well data is evenly dispersed

I am trying to measure how well scores from members of a group are dispersed over possible values. Think of it as a measure of diversity function. Thus, ...

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