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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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nested random effects in mixed effect models across different levels, and associated DF

I would like to fit a mixed effect model to the following dataset, but I am having difficulties figuring out the best way to define the random effects. For each subjects (...
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Degrees of freedom in Chi-squared test of homogeneity

Assume a contingency table $I\times J$, which consists of counts of multinomial r.v. with $I$ categories from $J$ populations with fixed marginal totals $n_{\cdot j}=\sum^I_{i=1}n_{ij}$ for each ...
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Understanding formula for Short Term / Long Term Degrees of freedom in minitab

Now I'm new to statistics, but the last time I did degrees of freedom, the formula I used was $df = n-1,$ but I've just been playing with Minitab and reading the help to files, and I noticed it is ...
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Chargaff's rule and degrees of freedom of the chisquare

I have a question regarding if and how one should take into account for the extra knowledge that he/she has of a model when determining the degrees of freedom of a distribution, in my case the chi-...
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Degrees of Freedom In Sample Variance

Recall the formula for sample variance $$s_{n - 1}^2 = \dfrac{1}{n -1} \sum_{i = 1}^n (\bar{x} - x_i)^2,$$ where $\bar{x}$ is the sample mean. There are many proofs for why $s_{n - 1}^2$ is an ...
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Why is there a change in the number of degrees of freedom when the following modification is made?

In the notes that I'm working through it says the following: "Let $X_1,...,X_n$ be a random sample from $N(\mu,\sigma)$ $$\sum^{n}_{i=1}\Bigg[\frac{(X_i-\mu)}{\sigma}\Bigg]^2$$ has a $\chi^2$ ...
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How to determine the df (degrees of freedom) in DLNM?

I am working on distributed lag nonlinear models (DLNM) for one of the problems. I have been going through the vignette provided to understand the concept in detail. I am trying to understand how to ...
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Building a Logistic regression with multiple dummies

I am building a model that has 10 dummy variables for a category called operator. The operator values are string, so I created binary variables to make sure each operator is within the model. I am ...
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Why is degree of freedom so important? [duplicate]

As far as I'm concerned, the degree of freedom is simply the number of linear equations need to be satisfied. However, it seems closely related to the statistical deduction. For example Dividing by ...
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Unclear “mathematical notation” in a polynomial

Although, the Enigma here is a protocol for enhancing the privacy in blockchain; however, the question is about mathematical notation, where we want to calculate the coefficients in a polynomial. ...
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ARIMA MODEL DEGREE OF FREEDOM PROOF

According to arima(p,0,q) model if we have n data and our total parameter is p+q then it is said that degree of freedom is n-(p+q). Could you mathematically demonstrate it? No sufficient information ...
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(How) can “de-meaning” help me solve this “clustering” issue?

I'm not particularly advanced when it comes to statistics and data analysis and have a problem I can't seem to solve. Basically, suppose you're doing school research and have three groups (to which ...
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Do generative models have less degrees of freedom than discriminant models?

I've read here that generative models have less degrees of freedom than discriminant ones, so they are more robust and less prone to overfitting. I would like to understand this statement with a ...
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Are degrees-of-freedom corrections necessary or possible for the exact multinomial goodness-of-fit test?

As the title: I have a discrete distribution with a small number of categories. I want to test if it is compatible with a parameterized distribution. If I were to do a chi-squared or G-test, I ...
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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 [closed]

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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385 views

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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58 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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124 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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1answer
55 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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79 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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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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30 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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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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125 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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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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231 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
127 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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39 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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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
56 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
118 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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27 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, ...