Questions tagged [degrees-of-freedom]

The term "degrees of freedom" is used to describe the number of values in the final calculation of a statistic that are free to vary. Use also for "effective degrees of freedom".

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Weird results from Chi Square test

I'm running a chi square test on some categorical values pertaining to race, and whether different racial groups participated in a clinic. As there's about a dozen different races in this data, I ...
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Which degrees of freedom estimate to use for two-tailed t-test?

I have two samples: Sample A = businesses that have not received a grant Sample B = businesses that have received a grant Ua = population mean of survival rate for businesses in A Ub = population mean ...
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Appropriateness of Chi Square in finding correlations in data set [closed]

I'm trying to determine correlations between different rows of categorical data in my given set. Different columns include race, sex, language, insurance type, etc., whereas the target variable is if ...
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Why does degrees of freedom = $\frac{\operatorname{Tr}(H'H)^2}{\operatorname{Tr}(H'HH'H)}$?

Wikipedia gives the following expression in "degrees of freedom" section, calling it the "Satterthwaite" approximation: \begin{equation*} \text{df}\approx \frac{\operatorname{Tr}(H'...
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How many "effective" observations from sliding window sampling?

I have data on the trajectory of a particle and am interested in the displacement of the particle in a given time period. In particular, I have information on how much a particle has moved in each ...
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Effective degrees of freedom for spline term in glmmTMB

I have fitted a model in glmmTMB that includes an spline function for age using the bs function from the splines package (version 3.6.2) in R. The syntax in glmmTMB looks like this: glmmTMB(...
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Degrees of freedom in emmeans package

This is my first time uploading, so please bear with me. I am currently trying to do a post-hoc test with three interaction term (time X support X NFC). We did a follow-up on participants' well-being ...
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Effective degrees of freedom concrete example of variable distribution with Ridge

I am reading a report where they used Lasso and penalty term $\lambda$. Below is a table presented: I have a question about the DF. The original model had 16 variables and no intercept, i.e without ...
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How to find effective number of degrees of freedom for time series

I have 10 years time series of daily precipitation and temperature data (3652 records) as given below: Date Precipitation(mm) Temperature (°C) 01.01.2010 20 12 02.01.2010 5 6 03.01.2010 0 9 ... .....
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Degrees of freedom of a coin toss

The probability of a fair coin landing heads is $p(H)=1/2$ and since there is only one other outcome we can deduce that the probability for tails is also $p(T)=1-p(H)=1/2$. Yet if we examine a ...
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Is it better to have more degrees of freedom or less?

The concept of degrees of freedom appears in many places in statistics. Yet I still don't understand what is the role of degrees of freedom. Why can we just use sample size (and we need to decrease it ...
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XGBoost when P>>N

Someone built an XGBoost classification model using each pixel in an image (256*256) as a separate feature, plus a few other features. However they only have 500 data points. The target classes were ...
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How are related "conditional F tests" to Likelihood Ratio test and Wald's tests in mixed models?

Let's assume there is a general linear mixed model with categorical covariates with several levels, so I want to test the main effects. Let's assume I want to test only the fixed part of the model. I ...
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"Degrees of freedom" of linear regressions

I would like to demonstrate mathematically a thing, but I struggle to do this since I'm not a mathematician and I only have some high school remains of maths - I'm only an evolutionary biologist with ...
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R: Inflated degrees of freedom in mixed linear model

I have a question regarding a mixed model I am using: In a study, participants have been presented with 40 different news article headlines and indicated for each headline whether they would share the ...
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How to deal with small degrees of freedom in an independent variable when testing for effects on continuous dependent variables?

I have a dataset of roughly 1000 measurements of body size in an invertebrate species collected from 15 different sites, with substantially variying sample size per site. Now I want to test how the ...
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variance estimation for fused lasso

In the paper THE SOLUTION PATH OF THE GENERALIZED LASSO the authors derived degrees of freedom for the generalised lasso. Assume that $y\in\mathcal{N}(\mu,\Sigma)$, with $\mu\in\mathbb{R}^{n}$ and $\...
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ANOVAs from SPSS and R report different degrees of freedom. Which are correct?

I am conducting a reanalysis of some data. The dv is continuous (beta value ie neural activity) and the iv is categorical (position) with three levels (1, 2, 3). There are 126 observations. The ...
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Specifying effective degrees of freedom (edf) of smooth to ensure nested GAM models (mgcv)

In section 4.10.1 on hypothesis testing of Simon Wood's text on Generalized Additive Models it states, "Note that strictly, the foregoing argument requires the approximating regression models to ...
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Is my understanding of the p-value correct?

Say we get some value $t$ from test statistic $T$ for a sample $X$ of size $n$. The $p$-value is the probability that under the null hypothesis $H_0$, we observe a value $v$ of $T$ that is at least as ...
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Degrees of freedom in an photon counting experiment for chi squared test

I am attempting to apply a chi-squared test to determine the goodness of fit between modeled and experimental data of a photon counting experiment. My data sets are two histograms, each with 75 bins. ...
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When I use the GLS estimation to analyse paired data, should I provide own degrees of freedom = number of pairs or leave the default?

Let's assume I have a repeated data study with 100 subjects. Now let's assume I have just pairs. I want to use the GLS estimation for it. Let's assume the compound symmetry residual structure, so we ...
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Degrees of freedom when comparing models applied in a secondary (test) dataset

Two models in R: mod_a = lm(height ~ age) mod_b = lm(height ~ age + sex) Those models have different degrees of freedom. Once they are applied in a separate set, ...
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Is it normal to have thousands of df in a logistic regression model?

I'll admit right off the bat that degrees of freedom is not a concept I understand very well in general. That being said, I was reading a study that reported the following results: I struck me that ...
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How to define degree of freedom for Ljung Box text?

I am using Ljung-box test after fitting an ARIMA model to a time series to investigate whether residuals do look like white ...
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Is there a way to correct for degrees of freedom when using a generalized linear model with a Poisson distribution featuring random effects?

I am running a generalized linear mixed effect model with a Poisson distribution to analyse count data. The model has a random effect that takes into account multiple observation obtained by the same ...
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What is $F_{k,\infty}$, i.e., $F$ distribution when the second degree of freedom approaches infinity?

What is $F_{k,\infty}$, i.e., $F$ distribution when the second degree of freedom approaches infinity? I'm wondering if there is a known distribution(such as $\chi_k^2$) that it converges to.
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Why do df.residual in R and df_resid in Python (statsmodels) produce different results? [closed]

The statsmodels result is consistently higher by 2. This is using lme4 (R) and MixedLm (Python).
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What Degree of Freedom should I be using for this Q-test

This is a Time Series problem. I am testing whether I have significance of residues at $lag=3$ using an $ARMA(1,1)$ model. From the $ACF$ plot, the autocorrelation of residues is significant. The ...
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Degrees of Freedom for Linear Combination of Variables

I have three mean estimates, all from variables assumed to follow a Normal distribution. The following is a mock example. x1 is estimated at 4, with a standard error of 5 and 6 degrees of freedom x2 ...
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huge degrees of freedom for post-hoc tests of lmer model using emmeans

I have a trial-wise linear mixed model with a categorial between-subjects factor group (A vs B) and two categorical within-subjects factors itemEmotion (neutral vs. negative) and neuralArea (frontal ...
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Degrees of Freedom for Variances in SAS Proc MIXED

Below is a SAS proc Mixed code generated by JMP. Both JMP and SAS give me a confidence interval for the variance components (in the table "covariance parameter estimates"). I would like the ...
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How to do a MANOVA if my three dependent variables have only two degrees of freedom?

In my experiment-design I have 3 dependent variables. They are related to percentages of time during which the subjects exhibit a certain behavior. As they always must exhibit exactly one of these ...
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Fit indices showing "na" in lavaan path analysis using DWLS

I am doing a path analysis using lavaan in R. I have two models of interest: Model 1. Model 2. As one of the variables in the model is ordinal, I specified the ordered="Y2" command when ...
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Large degrees of freedom (df) reported in lmer model

I am running a 3-way interaction linear mixed effect model using lmer function to see how reaction time varies as a function of age (older vs. younger), task (AJ vs....
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Satterthwaite degrees of freedom in cross-classified linear mixed models

My colleagues and I are running a few experiments using multiple stimuli and participants, where participants were asked to rate a series of targets that varied in perceived strength (strong, weak) on ...
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How did Acheson Duncan calculate degrees of freedom for ranges in his d2* table?

As found in Acheson Duncan, Quality Control and Industrial Statistics (and earlier), there is a table for d2* for estimating the variance from the range based on the number of subgroups and the ...
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Df calculations seem off in lmer with 3-level categorical predictor comparison

This is a MLM analysis of a physiological variable (so big dataset) with a time x condition fixed effect, where condition has 3 levels. Model code is: ...
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t-test with data in long-format including levels of non-interesting factor in R

I've computed an ANOVA with one between-subjects factor (2 groups each including 26 participants) and 2 within-subjects factors (item type with 3 levels and emotion with 2 levels) in ezANOVA. ...
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Confused about degrees of freedom

Everything I've read about degrees of freedom says more is better - it is an indication of a model's flexibility. I'm now running a power analysis in R and I've noticed that lower degrees of freedom ...
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How to calculate the degrees of freedom for L1 and L2 regularised GLMs?

My goal is to calculate various information criteria for generalised linear models (e.g., the AIC). To do this, we need to calculate the effective degrees of freedom of the trained model. In an ...
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Intuition for bandwidth and degrees of freedom in kernel smoothers

For Kernel smoothers such as local polynomial regression smoothers (the Nadaraya-Watson smoother), we consider $y = m(x) + \epsilon$, for $m(x)$ some smooth function we are trying to estimate and $\...
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degrees of freedom in estimation of sigma squared (HLM)

In HLM software, when running 2 level null model, its come out There are no degrees of freedom to estimate sigma_squared. Set sigma_squared to a constant, or delete one or more of the random effects ...
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Conflicting omnibus results for a mixed-effects model

I am attempting to get omnibus tests of interactions with a multicategorical variable ("strategy") in mixed-effects models. When running this in ...
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Degrees of freedom in conditional independence of categorical variables

I'm new to the concept of degrees of freedom and so far I only saw example of degrees of freedom in settings that are different from the one of this question therefore I decided to post my doubts here....
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Can one specify a fractional degree of freedom for a constrained parameter?

There is a good explanation of degrees of freedom elsewhere. But which heuristic applies in the following is not so clear from that explanation. There is also a different question elsewhere. Is there ...
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Why are degrees of freedom an issue for statistics only not parameters?

I just spent the last 2 hours trying to understand degrees of freedom, i read multiple interpertations, however one really stuck with me: it's the number of data points that are free to vary AFTER the ...
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Choice of Size of Latent Representations in Variational Autoencoders

Are there any guidelines concerning the choice of the size of the latent space when using VAEs? It does of course depend on the data. I found the following in Christopher Bishop's Book Pattern ...
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Welch-Satterthwaite equation for effective degrees of freedom

Using Welch-Satterthwaite equation to calculate the effective degrees of freedom i got 0.29, is that possible? What is the meaning of that equation and how can i know if I messed up somewhere?
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correct degrees of freedom

I want to compare two models via BIC in a regression. My conditional error distribution is gaussian. The existing model (not changeable) is: model 1: ...
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