The goodness-of-fit tag has no wiki summary.
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SK test for time series comparison or alternative?
I am evaluating the ability of the data derived from keywords typed in a search engine to detect outbreaks of a certain disease, by comparing it to the laboratory data for the same data. So I have two ...
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1answer
51 views
Goodness of fit in a GLM with scaled deviance
On this page, I am interested in the section “goodness of fit”, which is near the bottom of the page and contains the table of deviance functions.
The author states that the scaled deviance, i.e. ...
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Fitting mixture distributions and computing goodness-of-fit?
This question is a follow-up from a previous question of mine here. Thanks to @Glen_b, @gung and @rbatt for teaching me so many new things yesterday. It was mentioned in passing that mixture ...
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1answer
45 views
Testing the goodness-of-fit of a random distribution to a parametric distribution
I have a problem with a goodness-of-fit question.. I have this question I need to answer but I have no idea how:
Why do we need to test the goodness-of-fit of a distribution of a random phenomenon to ...
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1answer
74 views
Confusion with Chi-Square test
I have an extremely simple question regarding chi-square test. So far I have found two different formulas for it:
$$
\chi^2=\sum\frac{(x_o-x_e)^2}{x_e}
$$
and
$$
...
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Non-nested model verification
My questions are two fold:
Is there a generally accepted statistic used to compare non-nested, nonlinear models with different numbers of parameters? I'm thinking RMSE, but wondering what other ...
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1answer
57 views
How to see how good is my model?
I am using glm to find a model using training data and then use test data to see how well the model is behaving. My response variable is ...
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2answers
120 views
Whats the relationship between $R^2$ and F-Test?
I was wondering if there is a relationship between $R^2$ and a F-Test.
Usually $$R^2=\frac {\sum (\hat Y_t - \bar Y)^2 / T-1} { Y_t - \bar Y)^2 / T-1}$$ and it measures the strength of the linear ...
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How do I bin when fitting to power law?
I want to visualize the readership statistics on my blog posts, and see how well they fit to a power-law distribution. However, testing for power-law is notoriously difficult, so I wanted to ask for ...
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1answer
49 views
goodness of fit for contingency tables
I have a question on testing mortality table.
suppose I am given a simple mortality table.
...
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55 views
Why is it futile to use the deviance as a goodness-of-fit measure for Bernoulli data?
In Ordinal Data Modelling by Johson & Albert, page 102-103:
For Bernoulli observations [...] the asymptotic chi-squared
distribution of the deviance statistic may not pertain. Indeed, for
...
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74 views
Compare shapes with Kolmogorov-Smirnov test
I have two time series, both 100 points length: I would like to perform the goodness of fit to know if these two series have same or similar shape or if they differs significantly.
I have read about ...
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37 views
Power of chisquared test for large sample size
I would like to calculate the power of a Chi-Square test for goodness-of-fit as a function of sample size for a specified alpha-value (say 0.01). Specifically, I am referring to power as the ...
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1answer
115 views
Alternative to Pearson's chi-square goodness of fit test, when expected counts < 5
In a part of my research, I am fitting probability distribution models for the count data(and binomial data) using Poisson, Binomial, Negative Binomial and Beta Binomial models. I have few data sets ...
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266 views
How to visualize Bayesian goodness of fit for logistic regression
For a Bayesian logistic regression problem, I have created a posterior predictive distribution. I sample from the predictive distribution and receive thousands of samples of (0,1) for each observation ...
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1answer
48 views
$\chi^2$ parameter of a data fit
So what is that parameter. When I make a non-linear fit, the program gives me a value χ2/doF. What is it?
I know some statistics and I know those χ2 distributions are used for non-parametric ...
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86 views
Is the ANOVA lack-of-fit test valid for weighted regressions?
I'm working in bioanalytical chemistry and am trying to find a suitable lack-of-fit test for the calibration curve (predictor variable=concentration, response variable=analytical signal). The ...
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1answer
144 views
Chi-squared test for histogram data after doing an averaged shifted histogram
I have a data set of 903 continuous observations, that I graphically visualize with a histogram. The bin and width values could be optimized, but it is logical from the distribution that I have a ...
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1answer
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Will a quadratic and cubic latent growth curve model always have better fit than a linear model?
A conjecture that I have heard is this:
When you add a quadratic or a cubic term to a linear latent growth curve model, the fit will always improve.
Is this correct? Why/why not?
As I have had ...
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What is the relationship between R² and Log Likelihood?
I estimated a non-linear model using the MATLAB function @fmincon which returns me a Log-likelihood value.
I also estimate a linear model (OLS) from which I can compute the R².
Here I need to ...
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Fitting models to empirical data: do fits for random samples converge on the true fit?
I'm trying to fit a mathematical/theoretical model to empirical data, but the dataset is impractically big to fit all at once. (Specifically: I'm fitting a power law model using the methods of ...
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3answers
362 views
Comparing two vectors from negative binomial distribution in R
I'm using R and have two vectors of discrete values. They are not strictly speaking categorical because the values themselves are number of dots counted on the image of a cell (whole vector is all the ...
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1answer
193 views
High SRMR despite good fit based on other indices in SEM (latent growth curve)
Context: Latent Growth Curve Modeling for continuous variable with 15 time points. One intercept, two slopes (for first and ...
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1answer
88 views
Interpreting non-visual linear regression results
I'm using the GSL statistical package to perform a linear regression on two sets of numbers. I don't have a heavy statistical background, and I'm used to seeing regressions presented in visual ...
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2answers
334 views
Kolmogorov-Smirnov with discrete data: What is proper use of dgof::ks.test in R?
Beginner questions:
I want to test whether two discrete data sets come from the same distribution. A Kolmogorov-Smirnov test was suggested to me.
Conover (Practical Nonparametric Statistics, 3d) ...
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1answer
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How to assess the quality of a return period estimate?
Background
I have a time series of structural loads, which are measured forces on a moored ocean buoy, and I need to obtain the return period value so that the structure can be designed to withstand ...
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Real-time goodness of fit
I've to do a check of goodness of fit in real-time in my software but I don't know how to implement it: I've got a sum of weighted chi-squared variable with 1 degree of freedom. I can do the ...
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305 views
Measure of goodness-of-fit in Ordinal Logistic Regression with continuous independent variable
In case of the ordinal logistic regression, both of the goodness-of-fit statistics, Pearson and Deviance goodness-of-fit measures, should be used only for models that have reasonably large expected ...
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2answers
159 views
Model selection with nonlinear fitting? Statistical tests seem ambiguous
I'm working on fitting an exponential model
$\mathrm{Flux} = A+Bt+F\left(\exp(t_0-t/T_r) + \exp(t-t_0/T_f)\right)^{-1}+...$
to astronomical data (a light curve).
$A$, $B$, $F$, $t_0$, $T_r$, and ...
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1answer
136 views
Identifiying performance of individual feature components in accuracy of support vector methods
I'm using support vector regression (not classification) for a problem and it's working well.
However, in the older method that former lab members developed (a basic linear model, with weights ...
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129 views
Goodness-of-fit of model derived from multivariate logistic regression
I have a question regarding the relationship between the value of Chi square and df in determining the goodness-of-fit in a model derived from multivariate logistic regression. If the N= 290, Chi ...
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47 views
Comparing model adequacy across different dependent variables
I have a three-level factor that I want to model as a response. I can collapse this into a two-level factor and build a logistic regression model. I can also keep the three-way coding and build a ...
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507 views
Pearson's residuals
A beginner's question about the Pearson's residual within the context of the chi-square test for goodness of fit:
As well as the test statistic, R's chisq.test ...
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155 views
Calculate Efron's pseudo R-square for a tobit regression
I am calculating a tobit model using the vglm package. Is there a way to get the Efron's R square from the estimation ?
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Fitting a distribution with ties in the data
I'd like to fit some standard distributions, say lognormal, to a set of data which unfortunately has ties. The precision of the measurement simply isn't high enough. Of course you can still fit the ...
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Good CFA fit indices, but poor fit indices at structural equation modeling
I am currently working on my research and I have the following problem. I have conducted a CFA on all model variables and after deleting the troublesome items, the CFA yielded good fit indices.
...
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Residual, linear least squares and quality engineering
I wanted to ask this question on stackoverflow but I think it is more suitable here. If I am wrong, please tell me.
My question concerns the use in statistics to analyse physical/engineering data. As ...
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Can we use cross-validation to measure how well a distribution fits sample data?
Let's say I have a data set $X = [1,2,3,4,5]$. And I want to measure how close it is to a Gaussian distribution. Is there a way to use cross-validation to do this?
For example, if I do ...
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Why does log likelihood function for a model use SSE/n and not SSE/df?
I'm trying to find out how log-likelihood function works for linear regression. I found the formula here and here. Making some experiments with it (see code below), I was quite surprised that the ...
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1answer
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Finding anomalies in industrial part failures
I have a data set that is composed of the age an industrial machine part is when it fails (x variable) and the part's width in nanometers (y variable) at the time when it fails. The data looks ...
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166 views
About goodness-of-fit p-value and Pearson's $\chi^2$ statistic
In a simulation, I generate data from distribution A, and then I hope to test if each of some other distributions B,C,D... can fit the data equally well. Obviously there is an initial fit of the model ...
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Can I define an $R^2$-like measure in this way when predicting with exotic loss functions?
It is common in regression to see $R^2$ formulated as follows: $$R^2\equiv 1 - {SS_{\rm err}\over SS_{\rm tot}},$$ where $SS_\text{err}=\sum_i (y_i - f_i)^2$ and $SS_\text{tot}=\sum_i ...
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1answer
216 views
How to calculate absolute fit indices (RMSEA, GFI…) from relative ones (AIC, BIC…)?
I have conducted an IRT analysis with Conquest in order to compare two models (1-dimensional vs. 8-dimensional) applied to a given data set (41 items of a questionnaire, N=195).
Comparing the ...
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1answer
176 views
Goodness of fit for stock prices
I'm in my first days of learning R and hit a roadblock with a small use case from finance.
(EDIT) Basically I want to know how to test sample fitness against any ...
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2answers
128 views
Fitting parameters of a function
Imagine a graph where the x-axis is time in minutes (continuous) from 0 to 360. And the y-axis represents 'z' values. Of this continuous time course graph, I have 8 time points w/ their corresponding ...
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175 views
How to determine if one fit is significantly better than a slightly different fit?
Background: In planetary astronomy, the only method we have to estimate the age of a surface of a solid object in the solar system (other than Earth) is to identify craters. We then compare these to ...
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269 views
Equivalent of Kolmogorov-Smirnov test for integer data?
Is there an equivalent of the two-sample Kolmogorov-Smirnov test for integer data (not count data, as it can include negative integers)?
The Kolmogorov-Smirnov test does not perform well in the ...
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1answer
214 views
Polynomial in linear regression
I am new to Regression and R. I know that polynomial functions are used when a regression model does not fit data (underfitting), but I want to know which degree of polynomial should be used? I also ...
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1answer
430 views
How to read the the goodness of fit on nls of R?
I am trying to interpreting the output of nls(). I have read this post but I still don't understand how to choose the best fit. From my fits I have two outputs:
...
