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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.

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Model Deviance lower than Residual Degree of Freedom

I am trying to calculate the Variance inflation factor (VIF) for a Generalized Additive Model (GAM). The GAM model contains both constant terms and splines. The VIF is defined as Deviance of model ...
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Question of Degrees of freedom negative in SEM [on hold]

I have a "F_A_T_A_L E_R_R_O_R: Degrees of freedom is negative.", what can be the solution?
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Degree of freedom on Titanic Dataset

I am working on Titanic Dataset and I was trying to figure the relationship out between gender and surviving situation with Chi-Square Test. In a first glance, I said that there is four different ...
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Calculating degrees of freedom in a Mann Whitney U

I have completed a series of Mann Whitney U tests in R, and am looking for the degrees freedom. I'm comparing two datasets of n1=29 and n2=5, with StandardDev1 0.4525 and StandardDev2 0.3652. What ...
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What does the degree of freedom (df) mean in the results of log-likelihood `logLik`

After doing the regression using lm for fixed effect model or lmer for mixed effects model, I pass the results to the ...
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The exact value of Welch's t test degrees of freedom

Wikipedia defines an equation to approximate the degrees of freedom in Welch's t test and does not state anything about the exact value. Is there a reason why we could not evaluate the exact df and ...
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Why is 'degrees of freedom' defined in completely different ways for neural network and linear regression?

I'm trying to compare the statistical evaluation of neural network and linear regression. From some articles I found, the DOF increases with model complexity for neural network "Degrees of freedom, ...
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43 views

When is it ok to remove observations from a dataset

I have a dataset, equal to 135,997 rows and 9 columns, the head of the table looks like this ...
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55 views

How can RMSE be compared between a regression model and a neural network model?

In the calculation of RMSE, linear regression uses degrees of freedom(n-p) as divisor and neural network(feed-forward in my case) uses the total data number(does it have degrees of freedom as well?). ...
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Degrees of freedom in OLS regresison vs Bootstrap

I understand that in OLS, the degrees of freedom for estimating the variance of the residuals is n-q-1. We loose q+1 degrees because they are "used" to analytically determine the q parameters and 1 ...
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53 views

Are there always two degrees of freedom in any probability distribution?

Take any random variable $X$ that follows some distribution $P(X)$. I was looking at this Wikipedia page and I'm trying to get some intuition for why we choose to define standard moments the way we do....
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degree of freedom for natural n-spline

According to the statistical learning book ISLR (or ESL), we know that the degrees of freedom (df) for (common) $n$-spline (regression spline, based on the $n$-polynomial) with $K$ knots is $$(n+1)(K+...
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Using a t-test on distribution of a derived value

I have a data set of people making estimates with a lowest plausible, highest plausible and most likely values, with an estimate of confidence. I also have demographic factors (sex, age, education). ...
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Latent Class Analysis - negative degrees of freedom

I want to see how many profiles (latent classes) can be differentiated based on respondents’ patterns of responses to four binary variables (accepting or rejecting four different immigration policies)....
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Orthogonal contrasts, ANOVA, why are there only as many contrasts there are degrees of freedom?

For example, if I have the data $$ \begin{array}{l|l|l|l|l|l|l} A & low & & medium & & high & \\ \hline B & standard & new & ...
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Kenward-Roger degrees of freedom with lmerTest

I am trying to do a t-test with Kenward-Roger degrees of freedom on my linear mixed model with lmerTest in R. I found that there are two ways of specifying the degrees of freedom: either directly in ...
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In meta-analysis Q-statistic, is there a better way to compute the degrees of freedom?

I am working with a meta-analysis, and attempting to quantify heterogeneity across several data sources. I am using the following formula: $Q = \sum_i(w_i \cdot (y_i - \mu_F)^2)$ where $y_i$ is the ...
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Degrees of freedom when manually doing (Welch) T-test?

I have two samples A and B and want to test if the (Pearson) auto-correlation of A is greater than that of B. So far I've computed the two autocorrelations, $r_a$ and $r_b$ and found their standard ...
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Mean Square of Regression Error for categorical variables while computing F statistic

Give the annova table in the image below: I need to calculate the F statistic for the null hypothesis: b2 = b3 = 0 . b2 is cofficient of cylinder and b3 is the coefficient of doors. The formula used ...
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Degrees of freedom of likelihood ratio test with equal dimension on the null and the parameter space?

Let $x_1,\dots,x_n$ be iid samples from a $N(\mu,\sigma^2)$ and consider the hypotesis $$H_0:\theta\in\Theta_0,\,\,\,\,\,\,vs\,\,\,\,\,\,H_1:\theta\in\Theta _{0}^c$$ where $\Theta _{0} = \{\mu>0,\...
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Degrees of Freedom in Backward elimination

OK. I just had an exam and realized I made a mistake on a question and wanted to seek some guidance. The problem was essentially: "Use backward elimination to choose a set of predictors to predict ...
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inflated and inconsistent degrees of freedom using Satterthwaite's approximation with lme4 and lmerTest

In an unbalanced ecological dataset of 32 plots with 2 observations each, we conducted lmer-models on 3 different dependent variables representing abundances (individuals1 and individuals2) and ...
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Why effective number of parameters in K nearest neighbor is N/k?

Bellow is my deduction: According to the definition of k-NN fit, we have $$\hat{Y}(x) = \frac{1}{k} \sum_{x_i \in N_k(x)}^{N}= \frac{1}{k}diag(a_1, a_2,..., a_N)y$$ where $N_k(x)$ is the neighborhood ...
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Why error sum of squares has n-2 df (possibly not duplicate, please read on)? (Regression Question Series - Part 4)

In simple linear regression, the error sum of squares is given by $$ \text{SSE} = \sum_{i=1}^n(y_i - \hat{y_i})^2 \\ \hat{\sigma}^2 = s^2 = \dfrac{\text{SSE}}{n-2} $$ where $n-2$ is the degrees of ...
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how to make sense of the number of observations per parameters in deep learning models?

In a simple linear regression setting, it is common to talk about a minimum number of observations per parameter (which characterise the the degree of freedom). And it is easy to see that for multiple ...
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Explain why $df(S_{xx}) = 2$ [duplicate]

Consider $X = \{x_1, x_2, x_3\}$. Then $\bar{x} = \frac{1}{3} (x_1 + x_2 + x_3)$ with degrees of freedom, $df(\bar{x}) = n = 3$. Now consider the total variation in $x$: $$S_{xx} = (x_1 - \bar{x})^2 ...
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139 views

Why do we divide by the degree of freedom?

This might be trivial and vague question, but I still don't understand why when creating test statistics or estimators we always divide by the degree of freedom. Just to give examples of what I'm ...
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2answers
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Degrees of freedom for linear regression

I'm reading on a text book about linear regression, and when I thought I finally understood degrees of freedom, I found a statement that made me doubt what I know so far. Well it's in the context of a ...
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Degrees of freedom in simple linear regression (when bo is known)

I am wondering if you would be able to help me with some linear regression model problems. It is about a simple linear regression model and I am very confused with the degrees of freedom. Here is a ...
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What is the degree of freedom of semiparametric method for mixture distribution

In the semi-parametric method for density analysis, I want to compare one component semi-parametric mixture distribution and two components mixture distribution. Semi-parametric here means the shape ...
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SPSS identification restrictions on EFA models

I am trying to understand the restrictions used by SPSS to identify EFA models using ML extraction. FOr example the GFI for a 2 factor model of 8 items (shown below) has 13df I understand to identify ...
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1answer
50 views

Degrees of freedom correction in estimation of AR(p) process

Assume that I have a process $y_t$ such that $$y_t = c + \phi_1 y_{t-1} + \ldots + \phi_p y_{t-p} + u_t$$ where $u_t$ is i.i.d. white noise such that $E[u_t] = 0, \forall t$ and $E[u_t u_s]$ is equal ...
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1answer
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Repeated measures factorial assessed using planned contrasts

I have dependent data that can be arrayed as a factorial. I understand that although factorials can be assessed through ANOVA, it is not necessary or always desirable to do so. A second option is 1-...
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1answer
95 views

Understanding Kenward-Rogers Degrees of Freedom from lsmeans()

I'm trying to analyze data using a multilevel model which predicts subject response times using the experimental group and trial validity. ...
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Help - General linear mixed model in R [closed]

I'm in a bit of a panic at the moment. I'm writing a master's thesis and my supervisor did the statistical analysis in R. She fitted a general linear model to the data. Now, when reviewing everything, ...
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Should I correct the DF in the Li-Mak (1994) test?

I am doing diagnostic tests on a GJR-GARCH(p,q) model. I have carried out both the Li-Mak (1994) test and the Ljung-Box test, knowing that the latter was not made for GARCH models. The test statistics ...
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298 views

Why is N/k the effective number of parameters in k-NN?

For the sake of completeness, $k$-nearest neighbor method classifies a point in space by comparing the average over the labels of $k$ nearest neighbors with $0.5$. The book Elements of Statistical ...
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Is this model really saturated? Is there a good alternative to an ANOVA for saturated models?

I have chemical data from groundwater wells that were exposed to two separate amendments of vegetable oil and monitored over several time points. I am trying to set up a 2-way ANOVA to test if the ...
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1answer
440 views

Why effective number of parameters in K nearest neighbor is inversely proportional to K?

ESLII states that effective number of parameters in K nearest neighbor is inversely proportional to K. To get an idea why, note that if the neighborhood were not overlapping, there would be N/K ...
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Degrees of Freedom in ANOVA - same mean and same variance

When doing analysis of variance and making confidence intervals we work with a margin of error determined by quantiles from some distribution. Assume we have 3 groups and a total of 30 observations (...
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37 views

Linear combination of two non-independent random variables

I would like to check if the slope coefficients retrieved from two separate regression models are significantly different. Both models have the same independent variables. The dependent variable (DV) ...
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1answer
33 views

Why does a sample of n of a population of n retain degrees of freedom of n?

I understand that if you take a sample from the population that a single data point cannot freely vary if $\bar{x}$ is known and you have the remaining sample items. However, I do not understand why "...
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How to find the degree of freedom? [duplicate]

I have data from x number of groups, the actual data and the expected data. As I've understood it, the degree of freedom is the number of values that can vary. Is it then (x-1) (2-1)?
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57 views

Why the degree of freedom is NA ? And why the p value is calculated when the df is NA?

I used R to do the statistical analysis. After running a glm model, I used Anova function to look at the p value for each explanatory variable. So far, everything was normal. However, when I used ...
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Degrees of freedom for CSS ARMA(2,2) with intercept

This is something I'm been searching for a while now. I'm confused since when you estimate ARMA model by means of conditional sum of squares you are using a special case of maximum likelihood with ...
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Cox model with frailty (partial loglikelihood and df)

I am fitting a Cox propotional hazard model with a frailty term using the survival package in R. When I remove a fixed efect, I ...
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1answer
590 views

Calculating total estimated degrees of freedom for a GAM

I am trying to figure out how to calculate the total edf for a GAM. The model output is: ...
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The “generalized” Satterthwaite method?

Consider the one-way ANOVA with random effect. ...
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59 views

Degrees of freedom and T Test/Welch T Test

I teach A level and Undergrad Foundation Biology. We are applying 2-tailed 2-sample t-test for unequal variance (this bit is directly prescribed from the exam boards): $$|T| = \frac{|\bar{X}_1-\bar{X}...