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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“Reversed” Shapiro–Wilk

The Sharipo-Wilk test, according to wikipedia, tests the null-hypothesis ($H_0$) "The population is normally distributed". I am looking for a similar normality test with $H_0$ "The population is not ...
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20 views

When the null model performs better than more complex models

Consider a matrix $X \in R^ {n \times m}$ representing $n$ samples and $m$ features. Also consider a matrix $y \in R^{n \times k}$ representing $n$ samples and $k$ target values. $y$ has continuous ...
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1answer
20 views

Determining whether a successive instances are conditional or independent

I hope I can appropriately describe the problem. I have an example data set with 610 individuals with made up analogy (it's not really about cars). I want to determine the number of people have x ...
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2answers
52 views

Goodness of Fit Using $CDF$

I don't have a tremendous amount of experience with testing goodness of fit, and I've just begun studying it rigorously. A though occurred to me, and since it occurred to me, I'm sure it exists, and ...
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1answer
34 views

Test if two gamma distributed populations are different

I have data from two populations of different sizes. Both have Gamma distributions with different shapes and scales (as estimated in r): fitdistr(x/10000, "gamma") #186 members shape 0.586219900 ...
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77 views

How to Assess the Fit of Thousands of Distributions?

I have thousands of subjects, for each of whom I have a fitted gamma distribution, with the parameters estimated from each subject's data. It is easy to look at the distribution for one subject (say ...
5
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1answer
55 views

Finding quality of fit for two discrete variables with low statistics

I have data from an experiment which I am trying to explain using a model. I do not have an analytic formula for the prediction of the model but instead I got its prediction through a simulation. The ...
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1answer
54 views

Goodness of fit and which model to choose linear regression or Poisson

I need some advice regarding two main dilemmas in my research, which is a case study of 3 big pharmaceuticals and innovation. Number of patents per year is the dependent variable. My questions are ...
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11 views

Computation of likelihood of a simulated mean value being a part of population of observed mean value?

0 down vote favorite Would you please help me to clarify this question: I use a model to simulate milk yield of a population of animal (200 individuals), in each simulation I calculate the mean milk ...
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8 views

Computation of likelihood of a simulated mean value being a part of population of observed mean value?

Would you please help me to clarify this question: I use a model to simulate milk yield of a population of animal (200 individuals), in each simulation I calculate the mean milk yield ...
2
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0answers
62 views

When AIC and Adjusted $R^2$ lead to different conclusions

I hope it's okay to ask theoretically driven R questions here. R has given me the following results from my 'tournament of models'. All models are entirely distinct except from 3 basic control ...
2
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1answer
32 views

Simulated chi-square distribution doesn't match theoretical

Can someone explain why the distribution of Chi-square values I'm getting (using Pearson goodness-of-fit test) doesn't match the expected Chi-sqaure distribution? The test seems in this case to be ...
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0answers
17 views

How to evaluate the goodness of Fit of parameters obtained from EM algorithm

I have a set of observations $\mathcal{Y} = {Y_1, \cdots, Y_T}$. I am running EM algorithm to fit the observations to the following Hidden Markov Model $$A = [a_{ij}]_{N \times N}, a_{ij} = P(X_{k+1} ...
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1answer
28 views

Interpretation P value one sample KS test

I have some difficulties with understanding the output of the KS test in R. Suppose I want to test whether my data follows a exponential distribution with rate 1/117.5 with a significance level ...
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0answers
14 views

C-statistic for comparison of incidence rate poisson to cumulative incidence logistic models

I'm looking to compare the capacity of two models for predicting who does, and who does not, develop a certain infection during a hospital stay. Both models are based on the exact same patients, but ...
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1answer
44 views

Shapiro-Wilk test - are my data normal/non-normal?

Are my data normal/non-normal? How do you decide? I performed a Shapiro Wilk test and got the following results. How do you interpret this? ...
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0answers
30 views

Goodness of fit for multi dimensional scaling

What is considered to be an acceptable value for goodness-of-fit in multi-dimensional scaling (MDS). I tried to run an MDS analysis on my data with four dimensions in R. The goodness of fit comes ...
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1answer
23 views

Outliers and chi-squared goodness of fit

Do outliers lead chi-squared tests of goodness of fit to fail?
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1answer
34 views

Chi squared goodness of fit test

I have a dataset and I want to show that it has lognormal distribution by using estimated logmu and logsd of it by MLE. I have read about making dat into bins by using predetermined intervals, but I ...
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0answers
17 views

Goodness-of-fit test by Pearson's chi-squared test for bimodal normal distribution

Consider I have estimated the following parameters for two modes inside a vector of numbers: m1,s1 m2,s2 m is mean s is standard deviation I want to use ...
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0answers
22 views

Goodness of fit to poisson with unspecified mean

Is there a goodness of fit test for testing a series of counts against the whole family of poisson distributions? So, with the mean unspecified? Or does that not make any sense? Kinda related to ...
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1answer
82 views

Empirical Test for the Assumptions of Simple Linear Regression

Linear Regression has the below set of Assumptions, The Y-Values (or the errors, "e") are independent! The Y-Values can be expressed as a linear function of the X variable. Variation of observations ...
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18 views

Should I still compare my distrbution to others if I've found a fit?

I'm using the ghpy package in R to model some currency data. I currently comparing fits with the lik.ratio.test with the ...
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2answers
62 views

Meaning of significance level and critical values for kolmogorov smirnov goodness of fit test

I'm new to using goodness of fit tests and am encountering what I guess is a beginners misunderstanding of how the tables for critical values and different significance levels have to be read. I have ...
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1answer
38 views

Goodness of fit between actual values and non-linear model

I was wanting to get a goodness of fit similar to R^2 for a model I'm evaluating. The output of the model is one of 8 numbers based on environmental characteristics. This is not a linear model, so ...
4
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1answer
93 views

Should I find this big parameter suspicious?

I have some kind of disagreement with a groupmate. We have some data, and we have to fit a loglogistic distribution. Our highest data point is less than 14,000,000. The average of our data is ...
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35 views

Interpretation of logistic regression - Both Omnibus test and Hosmer and Lemeshow are p>.05

I was wondering if you could help me with interpreting a binary logistic regression with 6 or 7 predictors. Specifically, what does it mean when both the Omnibus test and the Hosmer and Lemeshow test ...
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1answer
48 views

D'Agostino-Pearson vs. Shapiro-Wilk for normality

In the field I work in, there is a large amount of impetus to use Shapiro-Wilk testing as the default normality test (possibly due to NIST and some pubmed papers). I understand that one weakness of SW ...
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54 views

Best goodness-of-fit measure to determine: is my dataset power law or exponentially distributed?

I would like to determine whether a discrete dataset that I'm modeling would be better fitted by an exponential function or a power law function. I'm aware that a chi-squared test may be a suitable ...
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1answer
43 views

High p-value Based on Residual Deviance when Model Appears to have Poor Fit

I'm running a logistic regression with R using the glm() function with family = "binomial" and a very large number of observations (37208). Only a very small number of observations have a true result ...
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2answers
74 views

Generate fake data consistent with adjusted R^2 pattern

Is it possible to specify a vector of adjusted $R^2$ values (or any other measure like AIC, BIC, $C_p$) for the set of all possible models in a data set, and then generate data that is consistent with ...
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33 views

Model selection in nonlinear fitting

Learning curves are fitted with multiple trendlines (exponential, power, logarithm). The fitting is performed by the Levenberg–Marquardt algorithm. So far so good. The question is, how to select the ...
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1answer
104 views

Post-hoc test for chi-square goodness-of-fit test

I'm conducting a chi-square goodness-of-fit (GOF) test with three categories and specifically want to test the null that the population proportions in each category are equal (i.e., the proportion is ...
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19 views

Metrics for regression error

Suppose I undertake a least squares regression on some data. I end up with a function such as $\hat{f}(x,y,\ldots)=\hat{\beta_0}+\hat{\beta_1}\cdot x+\hat{\beta_2}\cdot y+\hat{\beta_3}\cdot ...
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1answer
50 views

Are prediction and distribution-fitting ever not the same thing?

Intuitively, it seems to me that, if one is able to make accurate predictions about a variable, then one has also (perhaps implicitly) produced a good estimate of its marginal or conditional ...
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1answer
29 views

In testing a structural model fit, how strongly do the measurement models fit influence the overall structural model fit?

I am a beginner in SEM, sorry if this is an obvious question. But I have searched the literature and could not find anything that answers my question (except for this question: SEM: Do I still have to ...
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1answer
43 views

Chi-Square test: one-sided implementation?

I need to compare two samples and I would like to know if the distribution of the first stochastically dominates that of the second one. I'm not sure whether with the Chi-Square test I can verify ...
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1answer
84 views

Chi-square test p-value = 1

I am attempting to use the chi-square test as a goodness-of-fitness test in R, but I keep getting a p-value = 1. I expect a high p-value, but less than one. Can anyone point out what error I might be ...
3
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2answers
82 views

how can I test if a sample was created from a specific Discrete Distribution

How can I test if a sample was created from a specific discrete distribution. For example, if I have the following distribution 1- 0.2 2- 0.5 3- 0.3 and I ...
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What's the best way to demonstrate differences in these means/totals?

With some co-authors, I coded 200 video game reviews based on whether they mentioned any of nine different game elements. We now have the total number of times that each game element showed up in ...
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2answers
2k views

How to determine which distribution fits my data best (R)?

I have a dataset and would like to figure out which distribution fits my data best. I used the fitdistr() function to estimate the necessary parameters to ...
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13 views

Distribution of weighted data

I want to fit a distribution to weighted data, and I have some issues, starting with the parameter estimation. How can I perform the MLE with the WEIGHTED data? The histogram of the weighted data fits ...
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2answers
59 views

Finding the best fit continuous distribution

I'm an applied math graduate student with little background in statistics. I'm currently dealing with the following problem: I have a set of samples that I'm trying to fit a (continuous) distribution ...
2
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4answers
751 views

Why do I get this p-value doing the Jarque-Bera test in R?

Doing a Jarque Bera test in R I get this result: jarque.bera.test(rnorm(85)) data: rnorm(85) X-squared = 1.259, df = 2, p-value = 0.5329 Does it mean that the ...
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39 views

Confidence intervals for chi square goodness of fit

I'm having trouble figuring this out. I know that you calculate the confidence interval same as you would for a proportion, $p_i= P \pm 1.96 \sqrt{(P(1-P))/N}$, but in my notes it says: ...
2
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2answers
187 views

Test predictions of football scores against a null model of “no predictive skill”

So, I am trying to prove that I can predict football scores better than randomly assigning win,draw or loss. I have predicted 140 scores, I have succeeded at 67. My null hypothesis is that ...
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0answers
35 views

Find Weibull parameters from incomplete sample

I have samples with known number of missing elements (expressed as NaN's) that range from 10%-90% missing. The same function, Weibull, works for all cases. My question is then, how can I ...
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1answer
56 views

Fitting data to a Markov Chain

I am looking for the reference/toolbox/note on how to fit a finite discrete-time Markov Chain to given time series. Ideally, there shall also be criteria of whether the fit is good, and whether ...
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0answers
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Are my data normal? chi-squared for goodness of fit [duplicate]

I have been tasked with determining if my observed data follow a normal distribution. With 119 observations (continuous data from -4 to 4), I was able to create a histogram with 25 bins, and upon ...
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1answer
87 views

Goodness of fit for discrete data: best approach

The data: For the purposes of this question/communication we can assume the data looks like rnbinom(1000,size=0.1,prob=0.01) in R, which generates a random sample ...