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 Pearson correlation be used as a measure of fit?

In the context of multiple linear regression, is it acceptable to use Pearson correlation to discriminate how well a model fits a data set? Let's say that I have some experimental values that come ...
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17 views

Goodness of fit of a SUR model

I know that McElroy R^2 is a measure of goodness of fit for Seemingly Unrelated Regressions (SUR models), but how can one judge that the estimated equations are well fit by using the McElroy R^2?
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31 views

Generalization of one-sample Kolmogorov-Smirnov test for non identically distributed data?

Is there a standard approach for testing goodness-of-fit to a probability distribution when the samples are independent but not identically distributed? In other words, given the data $\{\{x_1, y_1\}, ...
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10 views

R: Shapiro-Wilk test with relation of W and P-Value? [duplicate]

I'm currently learning about the Shapiro-Wilk test for normality and using R for conducting simple experiments. One thing which is confusing me is that I found some results would produce a high W ...
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5 views

Chi goodness and Fishers: some theoretical issues post-experiment

I have run a simple experiment under four conditions: the Control, Technique A, Technique B, and Technique C (which is a+b) The dependent variable is compliance (e.g. Yes/No) These are my results ...
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23 views

How to interpret log-likelihood outputs from MASS::fitdistr (R)

AIM: Fit the best distribution to columns in a dataset (30k records) so that I can to go on to produce test data that is in a similar distribution. WHAT I'VE DONE SO FAR: Using R, I have found and ...
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1answer
42 views

PIT on a sample with m bins, and KS test used to estimate a good value for m

I know about PIT, but this works only when you know the distribution, or at least have a strong hint. What I am trying to achieve is to transform a given sample into an equivalent sample with ...
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56 views

Probability plot vs. QQ plot

What is the difference between probability plots and QQ plots when trying to analyse a fitted distribution to data?
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55 views

Kolmogorov-Smirnov test for large sample [duplicate]

I am investigating if an exponential distribution is a good fit for a large sample of data (200) I have. I have already looked at a histogram but was wanting to investigate further. I was going to use ...
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35 views

Is the Pearson goodness-of-fit test parametric or non-parametric?

In this question there was an interesting discussion concerning the Pearson goodness-of-fit test going on which was far from conclusive: Is there any statistical test that is parametric and ...
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79 views

Chi-square test: difference between goodness-of-fit test and test of independence

Concerning the Pearson chi-square test there seems to be a subtle difference between the goodness-of-fit test and the test of independence. What is confusing is that both tests seem to be calculated ...
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9 views

Goodness of Fit tests in a linear model (lin-log)

I am using a lin-log model and am currently doing tests for goodness of fit of the regression. I already used the R-squared test, Q-Q plot and Shapiro test. Are there any other tests i could use in R ...
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20 views

goodness of fit for censored data

How to estimate the goodness of fit of a sample containing censored values? There is some older work on the matter (here), but i'd like to know if there is anything more modern. I think a reasonable ...
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25 views

What does “$R^2$ estimates the combined dispersion against the single dispersion of the observed and predicted series” mean?

In a paper I came across the description of $R^2$ as "it estimates the combined dispersion against the single dispersion of the observed and predicted series". I am not able to understand this ...
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1answer
51 views

P-value NaN using chi2gof to validate lognormal distribution in dataset

I am trying to model a dataset of mine with a lognormal distribution using Matlab. I estimated the parameters via 'lognfit' and my generated datapoints with the fitted distribution look quite good ...
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22 views

Validity of an iteration for Goodness of fit to a specific application

I am not a statistics expert and would like to check the validity of a test I hav used on a survey results. Survey Results I asked people (n=264) to characterize a panoramic road they chose in 24 ...
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1answer
62 views

Testing that two models from two different data sets are independent

I have two different sets $(n_1=47$, $n_2=23)$ obtained under different conditions. I fit two different functions $(\text{Fu}_1$, $\text{Fu}_2)$ in MATLAB. $\text{Fu}_1$ was fit using the first data ...
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44 views

Compared results of 2 goodness-of-fit chi-square test

I am conducting Goodness-of-fit test on 2 cities using chi square. ...
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49 views

Goodness of fit tests robust against non-normality and estimated parameters

I'm struggling to find a goodness of fit test of the above. The non-parametric tests I have looked at (KS) seem to be unable to deal with estimated parameters - can someone help?
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32 views

Wrong parameters for GEV

I am doing some data analysis involving fitting datasets to a GEV distribution, but I'm getting some weird results. I'm using scipy, which uses MLE for fitting the parameters. My data is ...
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1answer
84 views

Statistical test for uniform distribution

I have a sample of 5 numbers from known interval [0, 10]. Is 5 numbers is enough to make some conclusions about whether these numbers are drawn from uniform distribution or not?
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1answer
78 views

$\chi^2$ test of significance vs. goodness of fit

I have 644 companies out of which 154 went bankrupt. I investigate below if the bankruptcy is related to the sector type: ...
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1answer
63 views

Logistic regression goodness of fit

I have fitted a logistic regression model showing the probability of flight given distance to a disturbance event. My sample size is 140 observations of which 45 were observed to fly. Distance to the ...
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32 views

Frequency Distribution Test Vs. Chi Square Goodness of FIt

I need to prove that the higher frequency of an occurrence within a particular range is statistically significant. Let me explain this with an example: X-axis has ages and Y-axis has the ...
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64 views

Linear Mixed Model Interpretation

I'm working on analyzing some data that need to use lme model, but I'm not sure about interpreting the output. Data looks like this: ...
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33 views

Reduced chi square goodness of fit

I often use the reduced chi squared as a quick goodness of fit test when fitting histograms. Is there an analogous method that works more generally for interpreting the absolute value of the best fit ...
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28 views

AIC, BIC: Multiple dependent variables

I have multiple candidate models, and each needs to be scored on multiple "metrics", where each metric is probability distribution. Essentially the metrics are like dependent variables. The question ...
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23 views

Multinomial goodness of fit

Suppose I generate a multinomial distribution with probabilities $p_i$, i from 1 to k. Now suppose I test it back using goodness of fit (chi square) with the probabilities we know. I read that this ...
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18 views

How to compare the fit of two tables of percentages?

I have two tables, you can think of them of results of two models. I would like to compare them to a benchmark to evaluate which model is a better fit. What statistical technique do I need to do this ...
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92 views

Is a weighted $R^2$ in robust linear model meaningful for goodness of fit analysis?

I estimated a robust linear model in R with MM weights using the rlm() in the MASS package. `R`` does not provide an $R^2$ value ...
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56 views

Chi-squared Goodness of Fit - very small expected values

I am trying to calculate chi-squared value for my fitted data using: $$ \chi^2 = \sum_i^n{\frac{(y-f(x))^2}{f(x)}} $$ where $f(x)$ are theoretical values from fitted function and $y$ are ...
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3answers
85 views

Combination of Data from Two Normal Samples not Normal?

I have two sets of data that hypothesis tests have shown to be normal and from the same distribution. I'm using MATLAB and for the way they give p-values, higher p-values suggest a better ...
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170 views

Lilliefors-Test and Jarque-Bera-Test results interpretation

I have conducted both of the above tests via the commands: lb <- lillie.test(x) jb <- jarque.bera.test(x) I think ...
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23 views

Comparing the Goodness of fit of two polytomous set of items not nested

I'm working on two identical set of items that only differ in their frequency-of-occurence dimension (in the first is max.7 while in the second is max.4). They are both fit with the Generalised ...
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A Sliding Goodness of Fit Method? (Foray into the Stats Community Wielding only R-Squared)

Thanks in advance for any help. I am a bit of a Stats idiot. I have two waveforms that I want to compare. One is an actual measurement, the other is a model of the first waveform which I calculate ...
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149 views

Evaluating goodness of fit for distributions (e.g. LogNorm, Gamma, …) with estimated parameters using KS tests (and R)

Currently I am trying to find a well-known distribution that fits to my positive skewed dataset (n=70) the best. First I used the fitdistrplus R package to estimate ...
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1answer
47 views

Null GLMM Poisson underestimate the mean of the response variable. Is it indicative of poor fitting?

I want to test the fixed and random effects of some covariates on a discrete variable with non negative values. In exploratory analysis I fitted a null Poisson GLM and an null Poisson GLMM. However, ...
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27 views

Logistic Regression with 1 independant categorical variable, goodness of fit

Suppose I fit a logistic regression model on some data with 1 categorical variable, suppose this variable can take 5 different values eg: Coutries, or cities Eg: NY, NJ, London, ..... Now, if I fit ...
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13 views

Goodness of fit for generalized linear nodel

How to measure the "goodness of fit" in generalized linear models for repeated measures. To make clear: I'm searching for something which is based on the (deviance) residuals, something like an adj. ...
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1answer
105 views

Logistic regression, goodness of fit interpretation

I'm having some trouble interpretting whether the model is a good fit. Below is an extract from some output from R. ...
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61 views

Obtaining sample variance from grouped data for goodness of fit test

This is a practice question I came across when dong some goodness of fit test examples.A company sells cloths by mail order.The size of clothes is defined by hip size; thus the height of customers of ...
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60 views

Expected Counts in Pearson's Goodness of Fit Test

A Common expression for Pearson's goodness of fit test is $\chi^2 = \sum_i \frac{(O_i - E_i)^2}{E_i}$ Where $O_i$ and $E_i$ are the observed and expected frequencies respectively. Now assuming we ...
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2answers
52 views

Is there any way I can manually set the intercept in SPSS?

As part of my dissertation I am looking into the relationship between temperature and methane emissions. A large proportion of this work relies on statistical interpretation and analysis. When ...
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2answers
78 views

Occam's razor (when is it appropriate to add another free parameter?)

So if I fit data to a function you can almost always decrease $\chi_{\nu}^2$ by adding more free parameters. However, this becomes ridiculous if you are fitting a 100-order polynomial to a straight ...
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67 views

Logistic regression with few observations

I suppose regression analysis with few observations has some peculiarities. Here are results for my logistic regression. $R^2_{\rm LR}$ = 0.7, Number of 1 = 6 (4 predicted), Number of 0 = 78 (all ...
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1answer
73 views

Interpretation of $R^2$ in fixed-effects panel regression

For cross-section analysis, $R^2$ represents the fraction of the variation that is explained by the model. I understand that a fixed-effects panel regression is designed to optimize for the "between ...
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66 views

Goodness of fit test for a normal distribution

In the example from the web site I was trying out this problem in page 107 about Goodness of fit test for a normal distribution.Question is about analysis of fat content of hamburgers. I understand ...
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1answer
46 views

Goodness of Fit Test for Logistic Regression with small n_i

I would like to test how well my model fits the data. The response is binary and the Chi-Squared Test cannot be applied for the residual deviance because the $n_i$ are $1$. To use the Chi-Squared GOF ...
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34 views

What's the best way to test the uniformity of location data?

I'd like a test to determine whether a number of collected 2D points (say, x,y in (0,1]) are distributed uniformly across the space. The points will be one or more 'paths' through the space - ...