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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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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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1answer
35 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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1answer
21 views

Planned contrasts in mixed models

My experiment consists of two factors, one between and one within subject. Time is the between-subjects factor and hold two levels: (low and high). Times is the within-subject factors and hold three ...
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37 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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27 views

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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1answer
52 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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28 views

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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11 views

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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22 views

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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1answer
23 views

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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26 views

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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1answer
28 views

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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19 views

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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16 views

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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31 views

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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13 views

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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29 views

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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1answer
46 views

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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72 views

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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28 views

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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19 views

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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1answer
66 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
62 views

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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34 views

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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34 views

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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0answers
5 views

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
18 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
9 views

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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0answers
13 views

Value at Risk of portfolio with student t distributed assets

I am trying to compute the VaR of a portfolio of cryptos, and trying to do it by 2 methods (VaR is defined as the minimum potential loss that a portofolio may suffer in the x% worst cases over a given ...
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1answer
57 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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0answers
22 views

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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0answers
20 views

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 ...
3
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1answer
209 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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21 views

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
328 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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11 views

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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0answers
34 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) ...
3
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1answer
30 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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0answers
10 views

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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1answer
49 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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0answers
126 views

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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0answers
39 views

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 ...
2
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1answer
422 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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0answers
39 views

The “generalized” Satterthwaite method?

Consider the one-way ANOVA with random effect. ...
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0answers
40 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}...
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1answer
565 views

Satterthwaite degrees of freedom in a mixed model change drastically depending on the DV

I have a couple of MLM models created using lme4: y1 ~ x1 + x2 + x3 + x4 + (1+x4|id) y2 ~ x1 + x2 + x3 + x4 + (1+x4|id) ...
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0answers
30 views

Why does increasing my number of levels in Random Factor ANOVA increase my statistical power?

In my Fixed Factor ANOVA I have 60 participants split evenly with two IVs with two levels in each IV (DF:1x1x1=1): IV1: Level 1: 15 IV1: Level 2: 15 IV2: Level 1: 15 IV2: Level 2: 15 But in my ...
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0answers
57 views

Count degrees of freedom in SEM with mean structures (latent growth model)

can someone enlighten me on how to calculate dfs for these models? I am very confused on how to calculate dfs with mean structures. Thank you!
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0answers
9 views

Extrapolating an aggregated feature set into the raw data

Background Say we create five products and for each product we send a survey out to 750 people (150 per product) and get them to answer a series of questions. One question could be "would you buy ...
3
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1answer
123 views

Dividing by degrees of freedom [duplicate]

When estimating parameters such as (I don't care about this specific instance particularly) Variance of a random variable X, one usually adopts Bessel's correction, i.e. using the formula $\hat{Var}{(...