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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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How many degrees of freedom in a T-copula is commonly used to model financial data?

I'm looking to fit some T-copulas to my financial return data. Unfortunately, the software I'm using can only fit a T-copula with a fixed degree of freedom parameter. So what parameter should I use? ...
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Selecting degrees of freedom in stepwise regression (stepAIC function in R)

Context: I have data available on water quality in a number of catchments, for example the concentration of Zinc (Zn). For each catchment, I also have a range of characteristics (n=16), such as the ...
Matt Tomkins's user avatar
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What is the motivation for the use of $n-m$ in the method of moments in Wedderburn 1974?

In an answer to this question Is there a Relationship Between Variance and Chi-Square? I wrote So to find the dispersion parameter, one has to use a different trick. In Wedderburn 1974 this is done ...
Sextus Empiricus's user avatar
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Degrees of freedom for biased sample autocorrelation function

I want to find the expression for the a biased estimate of the autocorrelation function for a time series $X$, and am doing this from the biased estimated autocovariance function for lag $k$, divided ...
hydrologist's user avatar
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Need help understanding degrees of freedom [duplicate]

I'm having a hard time understanding how degrees of freedom work. Considering this random regression model: $$Y_i = 2 + 3 x_i + \epsilon_i$$ I imagine using 4 datapoints. I decided to select $$x_1 = 2$...
Edward Ding's user avatar
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Why the Sum of Squares Error in ANOVA has n-1 degrees of freedom?

There is a statement that got my attention recently, which is "ANOVA is just linear regression". I was watching this video that seemed to explain the relationship between the two topics. At ...
rusiano's user avatar
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Difference in SAS PROC MIXED between DF when using type VC vs FA0(1) for one random effect model

I don't understand why the degrees of freedom (DF) are different between TYPE=VC and ...
Davor Josipovic's user avatar
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Effective degrees of freedom for residual variance in ridge regression

The definition of the effective degrees of freedom (dof) in Ridge Regression via the trace of the "hat matrix" is well known (see e.g. Hastie and Tibshirani's Generalized Additive Models). ...
Markus Loecher's user avatar
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Question about Degrees of Freedom in MANOVA

res <-manova(cbind(Sepal.Length, Sepal.Width) ~ Species, data=iris) summary(res) When running the above code, the result will be as follows: ...
user405858's user avatar
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Meta-analysis: estimating partial correlation coefficients using estimates from multi-level analyses

I would be very grateful if someone could offer some ideas or point to relevant literature on the calculation of partial correlation coefficients (PCCs) using estimates from multi-level analyses. ...
Mugen's user avatar
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Diebold-Mariano Revisited: what is a reasonable parameter count for information criteria when the model is complex?

Diebold (2015) wrote a follow-up paper/essay reflecting on how his work with Mariano to develop the Diebold-Mariano test has been abused over the years. One of the main points in the follow-up paper ...
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When does Satterthwaite-Welch's degree of freedom approximation break down?

Are there conditions when the usual formula to approximating the degrees of freedom in a Satterthwaite method breaks down? I realized I've never asked myself this anyway, and I was exploring ...
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Revisiting "Degrees of freedom"

In Eq.3 and Eq.4 of "effective degrees of freedom" paper Freedman defines degrees of freedom in terms of the difference between train loss and test loss, where train/test both use the same ...
Yaroslav Bulatov's user avatar
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ANOVA Puzzlement: huge Significance Shifts with Variable Type Conversions

My rowdata in R, as revealed by str() shows that: Variable A is of type character (chr), and variable B is of type numeric. Variable A has 4 levels representing solutions A, B, C, and D. I used as....
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Calculating Degrees of Freedom for Each Predictor/Coefficient in Logistic Regression

So I'm sure there's likely a simple answer here and I've just been thinking about this question for too long, but would appreciate your help nonetheless! I'm trying to calculate what the degrees of ...
dag48's user avatar
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How do you count degrees of freedom in multivariate distributions?

When dealing with a multivariate distribution (e.g., a multivariate t-distribution), how does dimensionality play into degrees of freedom? Let's say you have N measurements of a d-dimensional vector, ...
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Can you explain the logic behind degrees of freedom for interaction effect in multi-factorial ANOVA?

I am currently trying to build intuition for two-factor ANOVA by doing some simulation in Python, and some things are hard for me to parse. I have an ANOVA with 4 levels of one factor and 3 levels of ...
Eugene Krall's user avatar
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2 answers
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How to understand that there are n - 1 degrees of freedom in calculating sample variance? [duplicate]

According to Wiki: In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.[1] Estimates of statistical parameters can be ...
Steven Xu's user avatar
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CFA: chi-square value is 0 but with degrees of freedom

I want to do a SEM analysis with an actor-partner interdependence model in Mplus. I managed to calculate it and everything seems right if I look at the means, SD's, ...
Axenox's user avatar
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Sample size calculation for external validation of prediction model [closed]

I am confused about calculating degrees of freedom for external validation of a clinical prediction model. The calculation for sample size is as follows: We will include 4,875 patients. The ...
Komal Valliani's user avatar
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What are the degrees of freedom to consider for a G-test when some cells have expected values of 0?

Let's say I conduct a survey where people can mention their favorite color among four options (red, green, blue, yellow). After collecting the data, I create a contingency table crossing gender with ...
Daniela's user avatar
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Pooled Kurtosis Estimator Using Pooled Cumulant Estimators

I am trying to come up with a statistically sensible pooled kurtosis estimator that is based on pooled cumulant estimators. Specifically, I have unbiased estimators of the second and fourth cumulant ...
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Very small degrees of freedom when using yuen function in WRS2 package of R

I'm trying to run a number of independent samples t-tests. I'm using the yuen function in the WRS2 package because my data are non-normal and ordinal. My sample ...
Josie K's user avatar
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p-value of pearson correlation of correlated samples

I'm not completely sure if this question has been asked before, but I couldn't find one that suit my problem so far. So basically I am doing single cell analysis, and I have roughly > 100000 cells ...
Andreas Adinatha's user avatar
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Understanding degrees of freedom of F-statistic in Linear Regression

I was reviewing linear regression and I wanted to dig deeper into the F test that many software suites provide. I am aware that many sources comment on the degrees of freedom, but I haven't really ...
rusiano's user avatar
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Splines, logistic regression and sample size considerations

I have around 500 observations with a binary outcome at 25% prevalence and will be building an internally validated prediction model. I want to use splines to model non linearity in my continuous ...
blueberry's user avatar
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Sample covariance of t distribution and degree of freedom

If $X$ is a P by N size matrix, $X_{ij} \sim N(0,\sigma_i^2)$ if I standardize this X matrix with sample mean and sample variance (assuming I don't have access to the population mean and variance) I ...
maddy's user avatar
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Problem with dfs in multilevel analysis after converting data to long format

I have a bit of an odd problem and would love to get some suggestions of what the cause could be as I am currently at a loss: Some while ago, I had converted a dataset to long format in R using melt ...
jk12's user avatar
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How do I understand the calculation of degrees of freedom in the context of a 2 x 3 contingency table?

I am currently reading an article, Analysis of sensory ratings data with cumulative link models. In section 2.4 - example 1, the authors describe an experiment from Bi, 2002*: ... 25 subjects each ...
medium-dimensional's user avatar
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1 answer
352 views

Degree of freedom (df) in maximum likelihood estimate (MLE) for linear regression

I am reading Bain/Engelhardt's "Introduction to Probability and Math Statistics" about maximum likelihood estimate (MLE) for linear regression (p. 519 - 522). I first summarize 3 key points ...
Will's user avatar
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Using one linear model to test multiple hypotheses

Let’s assume the following: I have data of 100 subjects each performing 100 trials of a reaction time task At each trial, I measured the reaction time (RT) and a specific brain signal (BS) The RT and ...
drsternburg's user avatar
2 votes
2 answers
78 views

When calculating sample variance around a sample mean can I take degrees of freedom to be a fraction

Normally if you have $N$ samples of a random variable, from which you estimate both the sample mean and sample variance, you need to account for the missing degree of freedom in the sample variance: $$...
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Help with determining statistical significance of bees’ decisions [closed]

Firstly, my apologies for the basic nature of this question. I am numerate but stats has always befuddled me. I have had a look through earlier questions. I have installed a red mason bee box. It has ...
Russ's user avatar
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1 answer
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What is the reference edf for generalized additive models?

From the summary of my fitted generalized additve model (gam) I see two edfs. The first edf is the model edf and second is the reference edf. However, for AIC estimation, the reference edf is used. ...
Ly T's user avatar
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1 answer
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Optimizing Treatment Group Assignments

When setting out experiments, I want to make sure treatment groups are as balanced as possible. Instead of using randomization, I've started to use the following process. I first collect some ...
David Moore's user avatar
1 vote
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100 views

What is the critical value for those df not listed in Critical value table for Pearson correlation?

What is the critical value for pearson correlation df=190? The total number of samples is 192, so df is N-2 = 190. The tables have critical values for df 100, 150, 300, 500, 1000. If the df (N-2) ...
Karnan's user avatar
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What would be the sample number if two variables have different number of samples?

While correlating two variables, which have different number of samples in each, how can I find the df? Eg. Sample-A has 35 observations, Sample-B has 22 observations, How to calculate df (N)-2? ...
Karnan's user avatar
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3 votes
1 answer
699 views

Clarifying degrees of freedom in fixed effects model

I'm new to econometrics and learning about fixed effects. If I understood it correctly, we are literally including dummy variables for every observations. For example, I have a panel data of firms and ...
chunguc1004's user avatar
1 vote
1 answer
178 views

Results from extractAIC() from a mixed model lmer() are confusing

I have some legacy code in larger block of looped code that compares models. It essentially boils down to this similar example: ...
MrSwaggins's user avatar
1 vote
1 answer
85 views

Chi square reporting df for 2x1

I conducted a 2x1 chi square and need to report it in APA. There are 280 in the sample. Do I deduct the df from the sample size? e.g. X2 (1, N=279) Thank you
Maggie2018's user avatar
2 votes
1 answer
56 views

How to deal with potentially too few levels of the random effect

I built a linear mixed effect model with nlme with Body length, Habitat and Sex as fixed effects. Body length is added for body size correction while the other two both have two levels. In the random ...
Anna's user avatar
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2 votes
0 answers
120 views

Intuition behind rank of covariance matrix and testing hypotheses

I am trying to acquire some intuition about testing multivariate hypotheses where the test statistic involves inverse covariance matrix. As an example, suppose we have a $p$-variate random vector that ...
Richard Hardy's user avatar
3 votes
0 answers
152 views

When fitting a generalised additive model, how to choose how much to smooth?

When fitting a GAM, is there a rule (of thumb) for deciding if $k$ (max number of degrees of freedom for a spline) is large enough or not? How much should edf be below $k'$? And is that an absolute ...
user avatar
1 vote
1 answer
270 views

When transforming a dataset using the square root (or any other procedure), does the standard deviation of the dataset get transformed too?

Taking an introductory statistics course, and I am confused about the impact of a transformation on the df for a two-sample t-test. The df is dependent on n of each sample and SD of each sample, but I'...
Llove23's user avatar
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1 vote
1 answer
178 views

What should be the degree of freedom in ANOVA table

Consider the area under wheat for a sample of 44 clusters selected from 11 different villages. Four clusters were selected from each of the 11 villages and each cluster consists of 8 survey numbers(...
simran's user avatar
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3 votes
1 answer
186 views

Interpreting 'edf' from random factor smooth in GAM model

I specified a random factor smooth in the following way: ...
Christopher Dean's user avatar
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64 views

Implementation of Scheffe's adjustment in software

My understanding of Scheffé's adjustment for multiple comparisons is that it already adjusts for any possible contrast that one could make with the data, where the contrast coefficients sum to 0. ...
Michael Cooney's user avatar
2 votes
2 answers
732 views

Effect of sample size on Chi-squared distribution

As the degrees of freedom increase, the chi-square curve approaches a normal distribution. But what about increasing the sample size? If I am using degree of freedom =1, but with different sample ...
Baggins's user avatar
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264 views

Degrees of freedom in a 2^3 factorial experiment without three-way interaction included

I have an ANOVA model with 3 effects (A, B, C) with (a, b, c) levels each and 3 two-way interactions (AB, AC, BC). Within each cell there are n replicates. How to calculate number of degrees of ...
Lena 's user avatar
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1 answer
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Should I use `select=TRUE` for `mgcv::gam` while comparing df? [closed]

While running a GAM (Generalized Additive Model), I noticed that using select=TRUE inside mgcv:gam I get different ...
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