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".

Filter by
Sorted by
Tagged with
3
votes
2answers
95 views

finding out distributions mathematically

we know that the larger the degree of freedom, the less likely extreme events will occur (e.g., if you throw fair coin once, odds of heads is 50%, if you throw twice, odds of two heads are 25% and so ...
1
vote
0answers
13 views

LmerTest::lmer degrees of fredom incorret

I had a good search but apologies if this has been answered elsewhere. I am using LmerTest::lmer to estimate a mixed effects model. I have 50 subjects (in three groups) and two measurements per ...
0
votes
1answer
33 views

Where to find t statistic and degree of freedom in T test in Google Sheets?

I'm using Google sheets to find TTEST scores. Its outcome is a single value, namely, p value. But in addition to this p value I also need to report degree of freedom and a t statistic value: t(degress ...
1
vote
0answers
57 views

Interaction term alters degrees of freedom for main effects in glmmTMB model

I am using the glmmTMB package to test whether the probability of a seed remaining dormant in the soil (binary variable) depends on the population it comes from (fixed effect, 8 levels of population), ...
1
vote
2answers
46 views

Analogy between degrees of freedom in simultaneous equations and regression

Background: I went looking for intuitive explanations for degrees of freedom. I found some analogies that used simultaneous equations and constraints, others that cast them as independent data points ...
0
votes
0answers
8 views

Determining differences between hierarchical clustering groups with ANOVA: Is my method correct?

I have 20 different hybrids of plants (three replications each in a randomized complete block design), and I have taken measurements on subsamples within each of the plot. In order to see if there are ...
0
votes
0answers
17 views

What does replication mean for a mixed model?

I'm struggling to figure out how to test fixed effects appropriately in a mixed model, because of the concept of pseudoreplication (I have only seen this term in the fields of ecology and psychology). ...
0
votes
1answer
61 views

Meaning of “Error in contr.treatment(n = 0L) : not enough degrees of freedom to define contrasts” when adding fixed effects to nlme?

We are attempting to model and compare logistic growth over time for 6 different treatments using nlme. So far, we have successfully added random effects of ...
1
vote
1answer
43 views

Why $\frac{\chi^2}{number\,of\,data\,points - 1} \approx 1$ means good fit?

In my statistics class, I learned that if $\frac{\chi^2}{number\,of\,data\,points - 1} \approx 1$ the fitting of the model to the data points is good. I do not really understand why this statement is ...
0
votes
1answer
50 views

What does a lower bound do to the degrees of freedom of this random vector?

Consider two procedures to sequentially draw $4$ random numbers $(k_1, k_2, k_3, k_4)$ that add up to $100$: Procedure 1 can pick real numbers $\geq 0$ Procedure 2 can pick real numbers $\geq 20$ ...
1
vote
0answers
13 views

How are terms in SS (corrected sum of squares) independent?

What does the highlighted test mean? How are the terms not independent? Can someone elaborate in detail?
3
votes
1answer
180 views

Why no degrees of freedom for Z test

I am reading about hypothesis testing and have encountered Z test and T test. I have understood both the tests and their usage. One part that is not still clear is why does Z test does not depend on ...
0
votes
0answers
11 views

Is there any concepts for degree of freedom on dynamic system specified by differential equations?

We can fit covid19 data with SIR model (here is a good example). My question is how much data is needed to get a unique fit? Is there any concept for degree of freedom on dynamic system specified by ...
2
votes
1answer
106 views

Trace of the Hat Matrix in Ridge Regression

Generally, I know that the trace of the hat matrix ($H$) is equal to the rank of H since it is an orthogonal projection. If I wanted to show the trace of $H$ in ridge regression, would I be able to ...
1
vote
1answer
37 views

F-Distribution: difference between the expected value for a random variable and the expected value of its inverse?

It is known that the expected value of the F-Distribution depends only on the degrees of freedom associated with the Chi-square random variable in the denominator. In other words, E[1/X] does not ...
0
votes
0answers
29 views

Estimated degrees of freedom close to 1 in a GAM(M) indicate linear term; citeable reference?

I have several generalized additive mixed models that have smooth function terms with estimated degrees of freedom (edf) that are 1 or close to one. I have seen in several places such as blogs that ...
5
votes
0answers
200 views

What is Degrees of Freedom? [duplicate]

I have gone through tonnes of online resources (other stackexchange postings as well) and textbooks but still have not been able to grasp the concept. Most of them have vague explanations like "if you ...
0
votes
0answers
19 views

Degrees of freedom with categorical variables

I am constructing a Sequential ANOVA table using categorical variables. Variable $A$ has 2 levels, variable $B$ has 3 levels. I want to find the degrees of freedom for $A, B, A:B$ in the sequential ...
1
vote
0answers
24 views

How to calculate the ratio of observations to model parameters in a VAR(p) model

In machine learning, it's pretty common to use the general rule of thumb that one should have at least 10X as many observations as there are model parameters to avoid overfitting. As discussed here ...
1
vote
0answers
15 views

Finding Degrees of Freedom For Chi Squared Test proportions

There's a litany of other questionspreviously posted about finding df during a GOF test but I still struggle to understand it. I know that a way of thinking of df is to do (number of categorical ...
0
votes
0answers
9 views

Degree of freedom/sample size of a combined quantity calculated from several individual estimates?

Say I have data for CO2, CH4 and N2O emission in my experiment (having different experimental treatments). Each treatment means of either CO2, CH4 & N2O are calculated from 4 replicates (4 pieces ...
0
votes
0answers
22 views

How do you calculate the degrees of freedom for the chi-squared distribution for Pearson's chi squared test?

I am conducting the Pearson's $\chi^2$ test for three variables under the independence model. The data is in a $2 \times 2 \times 2$ contingency table. How do I find the degrees of freedom for $\chi^2$...
0
votes
1answer
31 views

Calculation of degrees of freedom for chi-square test

I am not sure how to calculate the df for the following data: The data is for a cross between flies to see if the observed phenotypic ratios are following the predictions of Mendel's laws. The total ...
0
votes
1answer
31 views

Is `p` in the formula for adjusted R-square defined for tree models?

Let $R^2$ be the R-squared defined for regression models. Given a vector x, the target, and a vector, y, the prediction of the ...
0
votes
0answers
27 views

Degrees of Freedom in Trading Moving Average (Open, High, Low, Close)

I have read "The Evaluation and Optimization of Trading Strategies" by Robert Pardo. He gave an example in page 293, of a moving average of CLOSE with 57 DOF. (50 MA + 7 trading rules/MA). He uses ...
0
votes
0answers
7 views

How do I go about choosing the right degrees of freedom for a simulation study?

How does one go about choosing the right degrees of freedom when sampling from a T-Distribution? I understand n-1 degrees of freedom is the theoretical rule of thumb, but my sample size is quite large ...
2
votes
0answers
30 views

Why am I seeing 0 degrees of freedom when testing main effects using lme4, but see 1 df when testing interaction?

So sorry if this is a dumb question, but I've been searching around and can't figure out what's going on. I'm running a mixed effect model with 2 fixed effects and random intercepts, as shown below. ...
1
vote
0answers
25 views

Degree of freedom of different distributions: Chi-Square Goodness of Fit Test

I try to understand why the number of constraints differ for the distributions in the table below, for the Chi-square goodness of fit test. I found the content in the following link. https://www....
0
votes
0answers
21 views

Why cannot the sandwich standard errors be used together with the Kenward-Roger denominator? [duplicate]

This question is about mixed models, and the use of both the Kenward-Roger correction (K-R) for small sample sizes and robust (sandwich) estimators for standard errors in the same model. Is it ...
0
votes
0answers
28 views

What is the equivalence of BETWITHIN degrees of freedom in mixed-effect models R?

As in the title. Let's assume I cannot use the Kenward-Roger or Satterthwaite method in mixed-effect models. I was told to use the BETWITHIN method. Now I switched to R. I can use any package I want. ...
1
vote
0answers
51 views

Why cannot the sandwich SE be used when the Kenward-Roger denominator df are in use?

This question is about mixed models, and the use of both the Kenward-Roger correction (K-R) for small sample sizes and robust (sandwich) estimators for standard errors in the same model. Is it ...
5
votes
1answer
341 views

AIC and its degrees of freedom for linear regression models

I have a dataset $S$ with $D$ features and three fitted linear regression models: Model1. Ridge regression that is fitted on all $D$ features from $S$. Model2. Ridge regression that is fitted on some $...
0
votes
0answers
19 views

About degree of freedom and model choice

I am re-examining an old problem of genetics. Between 1910 and 1925, the genetic model accepted for the AB0 blood groups (A, B, AB, and 0) was that there were two loci, L1 and L2, each with two ...
3
votes
1answer
120 views

DOF of Natural Cubic Spline

I am curious as to what the answer to the below question is? The question specifies a modeler has a cubic spline with knots at {10, 20, 30, 50}. They realize their model is overfitting at the ends of ...
0
votes
0answers
14 views

Contrasts Intutition Sum of Squares and Df

I am reading about contrasts for a class and at some point the formula for the sum of squares of a contrast is randomly stated. The author mentions then that constrasts display one degree of freedom ...
0
votes
0answers
24 views

How to determine degrees of freedom for regression when not all observations are independent?

I'm trying to determine the degrees of freedom for my dataset. (Purpose: to determine the confidence interval for the slope of the regression line.) The problem is, the explanations of degrees of ...
2
votes
0answers
90 views

Degrees of freedom in covariance calculation [duplicate]

When calculating the sample covariance, why do we divide by $n-1$ instead of $n-2$? Don't we lose two degrees of freedom since we need to calculate two sample means? For example, when estimating the ...
1
vote
3answers
111 views

Parameter estimation from single dynamic experiment. How many degrees of freedom?

I am estimating a parameter (diffusivity) from a set of experimental data coming from the same dynamic experiment: it can be summarised as changing the oxygen partial pressure around a solid and ...
0
votes
0answers
25 views

RCB ANOVA: Degrees of Freedom wrong?

I am running an ANOVA analysis on randomised complete block RCB design: 7 Genotypes 6 Blocks Ratings The model I am fitting is: ...
0
votes
0answers
12 views

Degrees of freedom in uncertainty budgets

While perfoming an uncertainty budget according to GUM, the degrees of freedom of each contribution must be determined. I have found in multiple sources online that by convention, type B contributions ...
2
votes
0answers
54 views

Bayesian MCMC inference with more free parameters than data points

I've come across Bayesian inference analysis with models that include more free parameters than observed data points (even up to three times more). It is my understanding that although Bayesian MCMC ...
2
votes
0answers
35 views

Why are my DF for denominator so large? Reporting mixed model output

I've never used linear mixed effects models before, so I'm new to reporting the results. Following a paper that used the exact same procedures as mine (pre and post test of this specific task), I'm ...
2
votes
0answers
29 views

Effective degrees of freedom for a booster? Complexity of a booster?

I was asked recently (in a job interview) about the complexity of a booster, and I had a decent intuitive answer, but I'm unsure about how to formalize it. Clearly it'll be a function of the ...
1
vote
1answer
22 views

Is there any benefit in reporting a model's regression and residual degree of freedom if I already report the no. of obs, F-value, RMSE, and R-sq?

Is there any benefit in reporting a model's regression and residual degrees of freedom in the regression results table if I already report the following: Number of observation used in the model ...
2
votes
1answer
137 views

Why is $\frac{\sum^n_{i=1}(X_i-\bar{X})^2}{\sigma^2}$chi-square distributed with $n-1$ degrees of freedom?

On Wikipedia, it says If $X_{i};i=1,\ldots ,n$ are independent normal $(\mu ,\sigma ^{2})$ random variables, the statistic $$\frac{\sum\limits^n_{i=1}(X_i-\bar{X})^2}{\sigma^2}$$ ...
1
vote
0answers
94 views

Negative degrees of freedom in multilevel SEM

Can someone please help me understand why I have negative amount of degrees of freedom in my output? I am doing a multilevel sem in lavaan and have 1 level 2 variable and 3 level 1 variables Thanks! <...
2
votes
2answers
72 views

Testing when the profile of a sample has changed - degrees of freedom?

I've been messing around with the Shannon index for diversity $ H' = -\sum_i^R {p_i \ln{p_i}} $, and it's associated 'evenness' measure $E = H'/H_{\text{max}}$. I'm trying to come up with a way of ...
0
votes
1answer
59 views

Degrees of freedom in matching for calculating p-value of t-score

I am running a matching analysis using the Match function from the Matching R-package. My sample includes 86048 firms, from which 611 have received treatment. After matching on sector(exact), number ...
1
vote
0answers
54 views

Why is the Degrees of Freedom 1 higher when model run with Poisson than Negative Binomial

Because the Negative Binomial distribution would result in there be an extra parameter to estimate the over dispersion, I am confused as to why I am getting a DF of 94 when I run the model with ...
2
votes
0answers
66 views

Significance of the parameter fitdf in Box.test

When reading ?Box.test, I learned about a rarely mentioned parameter fitdf, which specified the "number of degrees of freedom to ...

1
2 3 4 5
8