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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normality testing

What is the best method for testing for normality? I have a smaller data set today (30 in each group) and on the histograms none of them look normally distributed at all, whereas with the skewness ...
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Why does a goodness of fit test use the chi square distribution rather than the hypothesised distribution?

This is a homework(-like) question. I know the answer but don't understand it. If we were to answer the question "Are 5 different groups of mammals equally common?", what test would you perform? ...
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interpreting the clogit output in R

Maybe this is obvious but I've never done a conditional logistic regression before. In the clogit output after the Rquared value there is a max possible value. I assume this is max possible Rsquared, ...
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35 views

How to choose the best logit model using step function in R

I have the data below. I was wondering how I could choose the best model fit of logit model using step function in R. Here is the data in R format: ...
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9 views

goodness of fit gamma distribution matlab

I have a set of observations obs. If I plot the histogram of the observation I see that they could come from a gamma distribution ...
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49 views

Fitting a Gaussian to a histogram when the bin size is significant

I'd like to fit a Gaussian to some experimental data that is binned (the binning is a result of the physical limits of the device). Importantly, the bin size is significant enough that the gaussian ...
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How to know if “best fit line” really represents known set of data?

I have a known set of data. I have created a "linear best fit line" for that set of data. Is there a way to determine how well my set of data fit that best fit line (some sort of score)? I'm very ...
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1answer
17 views

Log Linear Models: Interpretation when None Fit

This is question 9.6 from Categorical Data Analysis by Alan Agresti (Wiley, 2013). The question asks us to find a Log Linear with the best fit for a 2x2x2 contingency table. The following are the ...
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29 views

Goodness of fit test for bivariate circular distributions

I'm trying to implement a goodness-of-fit test for a bivariate distribution on the torus. In the univariate case, i use the distribution function to transform the data so it presents a uniform ...
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16 views

How can I evaluate binary response models that have weighted observations?

I'm working with a binary response data set, but the importance of each observation varies over a factor of 100. Models to fit the data can accept a weight for each observation. But when it comes time ...
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Goodness of fit for a spatial panel with fixed effects and both spatial lag and spatial error

On a dataset, I performed spatial panel regressions with fixed effects, and with both a spatial lag and a spatial error (both are significant), using package splm in R (Millo and Piras 2012 Journal of ...
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25 views

How to measure goodness of fit in a simple quadratic Gaussian GLM?

I hope this question will be specific enough, I went through many of the other questions about GLM but now I am even more confused because my sample size is small and it seems that R square (or pseudo ...
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9 views

Should the rivals models include the same number of observed variables?

The question is about comparing models that include different number of observed variables. For example consider I have an 80-items questionnaire and I want to do confirmatory factor analysis (CFA) in ...
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1answer
27 views

Is there any Goodness of fit tests for Vine copulas?

Is there any goodness of fit tests like those based on probability integral transform (PIT) of Rosenblatt available for Vine copulas as a built in function in R? I know we can use ...
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28 views

$R^2$ (coefficient of determination) and linearity in multiple linear regression

For simple linear regression (SLR), in order for $R^2$ (the coefficient of determination) to be a meaningful measure, it must be true that $X$ and $Y$ are linearly correlated. Specifically, $R^2=r^2$, ...
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1answer
168 views

Logistic Regression with regression splines in R

I have been developing a logistic regression model based on retrospective data from a national trauma database of head injury in the UK. The key outcome is 30 day mortality (denoted as "Survive" ...
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26 views

poor Fit Indices

i am facing problem in getting the good fit indices. my sample size is 236, i have 4 latent variables(A:3component each:4, B:1 component 4item, C:1 component 4 item, D: 3 component each 3-4) so 31 ...
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Tracy-Widom distribution - Phase transitions - catastrophe/chaos - 'surface-fit'/'curve-fit' software

Is there an algorithm to determine the fit of a sample set of data to a saddle curve? I'd like to know the variance from the closest fit the sample has to: \begin{align} z &= x^3 - 3xy^2 \\ z ...
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33 views

Inflation of Adjusted R2

Consider the case of a multiple regression model, with about 10 regressor and very few observations (about 15). I have to choose 10 out of 20 available regressors, to be included in the model. In many ...
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Can factor analysis improve the fit of a predictive regression model?

My company is working with a client who have built a logistic regression model to predict whether kids with psychiatric disorders will successfully complete a State intervention program (Yes or No). ...
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75 views

Power-law fitting and testing

I want to test the distribution that best fit a specific metric (that I call SD) extracted from the source code of systems. I have a guess that they follow a power-law behavior. My sample: 20 ...
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1answer
41 views

Goodness of fit: observed vs simulated data

I have a set of 2-dimensional "observed" data of sample size N: $$O = \{(x_1, y_1), (x_2, y_2), ..., (x_N, y_N)\}$$ The hypothesis is that $O$ is a realization of ...
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1answer
35 views

Assessing residuals from a regression model

I am trying to understand what the residuals from a regression convey about the model's adequacy/ability to explain the variance in the data. I read that if we are able to take the residuals from a ...
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1answer
21 views

AIC: relative versus absolute predictive error

I've read two interpretations of Akaike's Information Criterion (AIC) that seem to be in conflict, and I was hoping that someone could help me understand how to reconcile them. Interpretation 1: ...
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1answer
44 views

Root Mean Square error (RMS) to compare two solution methods?

I solved nonlinear reaction diffusion equation in two method, and I want to make comparison between my outputs by using RMS error. The first solution is $u_1$, a $21\times 21$ matrix, and the second ...
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1answer
44 views

How to test if many samples are from the same distribution

For each day of the week I observe $n_i$ independently chosen values from some process. I would like to be able to answer the following two questions. Are the distributions from which the samples are ...
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1answer
102 views

How to evaluate the goodness of fit for survial functions

I am a newcomer to survival analysis, although I have some knowledge in classification and regression. For regression, we have MSE and R square statistics. But how we can say that survival model A ...
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chisq.test with R

I want to do a Goodness-of-Fit test of my data and the Weibull-distribution. I have estimated the Weibull distribution using the survreg-function in R. Now I want ...
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20 views

Partial pseudo $R^2$ with GLMs

Is a partial pseudo $R^2$ (pseudo $\eta^2$?) even a valid concept when dealing with a GLM? This, of course, presumes that partial pseudo $R^2$ is valid at all. If it is valid, how would one go about ...
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1answer
53 views

Chi-Squared Goodness of Fit Test Alternative? - Zero Can't Be in Denominator

I have 5 zones(categories) in which a certain percentage of total sinkholes exist. I have 5 different maps that I am testing to see which one provides me with the best fit to my expected percentages ...
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Please help me interpret this goodness of fit test

In the game of Bridge, 52 cards are distrubuted randomly among 4 players, each player ending up with 13 cards. I implemented a random number generator using the RNGCryptoServiceProvider form the ...
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22 views

Goodness of fit index in HMM

I am working on a dataset which I am training using the Baum Welch algorithm in order to produce an HMM. Because of the fact that my dataset is rather small I am using Leave-one-out cross validation ...
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1answer
77 views

Goodness of fit for nonlinear model

We have fitted a nonlinear function to observed data. The next step should be the assessment of the goodness of fit of this function (like $R^2$ for linear models). What are the usual ways to ...
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Chi-squared calculation for (nonlinear) model goodness of fit for data with trials

I would like to be certain of how to calculate the $\chi^2$ value for this scenario: We desire a measure of the goodness of fit of a nonlinear model to a data set. The data consists of many ...
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Evaluate goodness-of-fit of estimation of Pareto-like distribution

I would like to evaluate the goodness-of-fit of the following (Pareto-like) distribution: $$ f(r) = \sigma \centerdot r^{-\rho} $$ The function estimates the population of cities given the rank $r$ in ...
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Distribution hypothesis testing - what is the point of doing it if you can't “accept” your null hypothesis?

Various hypothesis tests, such as the $\chi^{2}$ GOF test, Kolmogorov-Smirnov, Anderson-Darling, etc., follow this basic format: $H_0$: The data follow the given distribution. $H_1$: The data do not ...
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VECM “goodness of fit” in R

I'm using ca.jo in R to perform the Johansen test on a given dataset. I obtain my VECM coefficients, cointegration rank, etc. However, it does not seem to give any notion of "strength of ...
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1answer
47 views

How to test if some data points is drawn from a distribution with linear PDF?

I have some data in the range [0, 1], and from the histogram below, it seems that they might be drawn from a distribution with linear probability density function (what's the name of that kinds of ...
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1answer
53 views

Understanding scipy Kolmogorov-Smirnov test [duplicate]

I'm trying to understand the Kolmogorov-Smirnov test using a very simple example. I generate a set of random, uniform values between 0 and 1.0. I then test that these values are from a uniform ...
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How to justify a distribution fit is good

I've got 5 datasets to which I would like to fit a model distribution. I'd like to use the same distribution for each dataset but with different parameters. So I use MLE to compute the best parameters ...
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Calculating $R^2$ two different ways

I am calculating my $R^2$ for a model two different ways. I used pred = predict(model, newdata = mydata, se.fit = T) and then calculated ...
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47 views

F-adjusted Mean Residual Test in R

I'm running diagnostics on a logit model in R produced with glm(formula = formula, data = data, family = "binomial"). I'm ...
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37 views

Am I using Goodman-Kruskal gamma or Somers D or Kendall tau correctly and what do they mean?

I am seemingly blindly following this publication that has done work very similar to what I need to accomplish (page 18-21). My analysis is a multinomial logistic regression where I have 3 possible ...
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1answer
103 views

Interpretation of multinomial logistic regression output from R

I have used mlogit package and I am trying to summarize the results I have from my model. I have a question regarding the reference value and will get to that in a ...
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1answer
24 views

Distribution comparison across different treatments

if I have a table like this In which, site = different sites of measurement (tissue or organ) type = different types of virus And I want to ask something about the data 1.What test can I use to ...
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Why is $R^2$ poor for AR model selection used for forecasting?

There is a related question here, about how to calculate the R-squared on a regression with ARIMA errors. I found the answer quite useful, and hoped for some elaboration, particularly on Rob's closing ...
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Figuring out the fixed characters in (for example) a ISBN number

I'm trying to remove positions that contain fixed values from strings of random data. An example is removing the string "ISBN" from a book isbn code without prior knowledge of that being a fixed ...
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1answer
122 views

Anderson Darling exponential distribution

I need a goodness of fit test for the exponential distribution. I understand that Kolmogorov-Smirnov is not generally regarded as very powerful and that Anderson-Darling is regarded as superior. ...
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Goodness of fit (Kolmogorov-Smirnov) test for a time series?

This is a somewhat basic question, I guess. I have a sequence of random variables $X_1,\ldots,X_n$ that I believe to be i.i.d. uniform on $[0,1]$. Being i.i.d. uniform corresponds to my model ...
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139 views

Fit measures for GMM Arellano-Bond estimator in R

A colleague and I have been working with difference GMM, i.e. the Arellano-Bond estimator, in R. Our option has been to use the pgmm command from the plm package. However, now I am struggling to test ...