Questions tagged [non-independent]

Data, events, processes, etc, are non-independent if knowledge of 1 provides some information about the state or value of the other.

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MANOVA for equal sample sizes, non-independent samples, and heteroskedasticity for time series data

I am looking for a MANOVA-like procedure testing for equal mean vectors for populations that allows for dependent samples (probably because the data are time series and the vectors are correlated), ...
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2answers
65 views

Correlation of two continuous variables but with clustered data

I want to correlate two changes in time, a change in microbiota with a change in some marker. There are several time points, so I have several differences in each participant. My idea is to see if ...
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Interpretation of Coefficients if Dependent Variable are Residuals from Another Regression Model

I try to model daily stock market trading volume with a bunch of independent variables like stock returns, stock price volatility, etc. in a time-series regression model. In the first place, I ...
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1answer
32 views

Determining whether the mean of a set of non - independent values is statistically different from zero

There are some areas of statistics that I am fairly confident with, and others, that are probably very simple that I am fairly clueless about. Only one way to go but up though. I have the dataset ...
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1answer
20 views

Dependent variable with negative values

Using a questionnaire, I quantitatively obtain the value of a symptom in a patient (that is, an ordinal variable). I apply this questionnaire twice, these occasions are separated by a period of one ...
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32 views

Which test to use? Independent data or not?

What I have is a cross section of a bone divided in 60 equal slices. These 60 slices form 4 groups of 15 slices each corresponding to the 4 anatomical orientations (anterior, lateral, posterior and ...
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5 views

ICC (intra-class correlation) for a frailty model

Is there a way to estimate an ICC from a frailty model, such as that shown in output 89.11.5 in SAS phreg's documentation Example 89.11 Analysis of Clustered Data (link below) ? https://documentation....
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1answer
11 views

Ideal copula family to evaluate a joint CDF of a process with non-linear dependency?

Say a process exhibits ARCH/GARCH type non-linear dependence and we wish to evaluate its joint CDF. Without relying on a criterion, such as AIC what is the best copula family that fits this framework? ...
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1answer
48 views

Variance of the mean of correlated variables

I am totally puzzled by this one. Let's say that my data is $X \sim MVN(\mu,\Sigma)$ where the variance-covariance matrix $\Sigma$ is of size $m \times m$ and is constructed in such a way that all ...
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1answer
47 views

How to reason about independence of combinations of events?

Suppose sets $A , B,$ and $D$ are independent. Is it guaranteed that $A \cap B^c \cap D$ is independent from $B^c \cup D^c$? Isn't $B^c$ ($B$ complement, or $B$ not happening) giving me ...
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Factor analysis structured with a dependent variable (not independent variable)

A model from the social sciences has been suggested that income inequality (as a dependent variable) "causes" a range of downstream independent variables including teenage fertility, obesity etc. ...
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18 views

Distributions over sequences of non-independent Bernoulli random variables

I'm modelling the generation of some sequences using random variables for generation of their components. For instance, the probability of generating the sequence $ABC$ should depend entirely on $P(A) ...
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Get confidence bound for dependent observations

I have created a metric which is basically a way of assessing performance of an individual by looking daily at the performance and compare to the performance level before the individual started. So ...
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1answer
18 views

Comparing the predictive power of two non-independent ordinal independent variables

I am looking to compare the predictive power of two ordinal independent variables (RA & 0.5RA+0.5RM) on success (please see image). These independent variables are not independent of each other.(...
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1answer
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Let A and B be two random variables, both independent from another random variable C. Is A*B also independent from C?

Let A and B be two random variables both independent from another random variable C. If A is independent from B, is A*B also independent from C? And if A and B are no independent from each other?
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Discrete distribution for a series of dependent bernoulli trials

Situation: I have a dataset which shows the number of independent observations of an event which took place after a certain waiting time has passed. To give a more plastic example: I observe the death ...
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20 views

Multiple comparisons and non-independent tests in prevalence data

Thanks in advance for all and any help. I have tested six different species for a disease on both an island and a mainland region. I wish to compare the prevalence of the disease between the island ...
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1answer
103 views

Response consists of pairwise distances: how to address non-independence?

How to deal with situations in which the response variable consists of pairwise differences within each experimental treatment? Here are two examples to put my question into context: pairwise ...
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1answer
44 views

Cumulant of sum of correlated random variables?

Let $X,Y$ be two random variables. We denote by $[X^k]$ and $[Y^k]$ the $k$'th order cumulants of $X$ and $Y$, respectively. I'm interested in computing the $k$'th order cumulant of $Z = X+Y$. If $X,...
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1answer
34 views

Making naïve Bayes less naïve by accounting for mutual dependence

I'm playing with the pet example of figuring out the probability someone has the flu given certain symptoms, namely fever and nausea. Let's define our priors, considering the "probability of x" as ...
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1answer
18 views

Why can the null and alternate hypotheses of McNemar's test be written in terms of dependance/independance of tests?

Consider a study to examine whether food frequency questionnaires and three-day food diaries are equally likely to label a women as consuming less than the RDA of calcium. Because calcium intake can ...
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1answer
92 views

Mixed Effects Model (3 level model?)

Consider the following problem. The dataset that I am considering has $n=1800$ units (high-end copying machines). Label the units $i = 1,\dots,n$. Unit $i$ has $n_i$ recordings. It is of interest to ...
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Alternative to Poisson process with non-independent events?

Correct me if I'm wrong but as far I know, a Poisson distribution assumes the events are independent of each other. I have a dataset of events over several years where the occurrence of an event may ...
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No of trials needed for a dependent event

I am from risk management. An event is defined as a system going down. Issue is a vulnerability in the system. Higher the severity of the issue , greater the probability that system is going down. ...
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12 views

Chi2 versus other tests for dependent samples (same observer different time)

I have come across a problem at deciding which hypothesis test I should use. I have personal previous research (great part of which is lost); of it, I have all the n and the proportions for each ...
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Statistical Test Accounting for Multiple Limbs Per Subject (correlated, non-independent data)

I'm analyzing a small dataset (n~100) where patients are counted twice at the same point in time - once for a right limb, and once for a left limb. In other words, the sample is correlated. I want ...
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Interpretation lm R independent categorical variable

I understand how to interpret dummy variables etc., but I have got trouble of interpreting a independent categorical variable. This is my output: ...
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1answer
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Is it possible to have dependent and exchangeable random variables? [duplicate]

Is it possible to have dependent and exchangeable random variables? Someone told me yes.
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29 views

Low sample size with independent observations

I am looking at sports team level data (summarized by average in each season) over several seasons and would like to predict/classify the winner of the championship. In a single season, the data has ...
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1answer
72 views

Seeking an intuitive understanding of independence for random variables

I'm trying to gain a deeper, more intuitive understanding of what it means for two random variables $X$ and $Y$ to be independent. From my statistics courses, I know that $X$ and $Y$ are independent ...
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Calculate AMH copula parameter given kendall's tau

I am trying to find a way to calculate the parameter $\theta$ for the Ali–Mikhail–Haq (AMH) copula when given a value for Kendall's Tau, $\tau$. I am trying to do this in R and have thought of using ...
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Hypothesis testing using non-independent distributions drawn from the same model

The explanation that follows is a simplification but preserves the key details (I hope). I am working on a problem related to hypothesis testing using results from a numerical hydrodynamic model of ...
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1answer
67 views

Expected value with dependent samples

It is well known that the expected value of a function can be approximated with i.i.d. samples: $$ E_X[f(X)] = \frac{1}{n}\sum_{i=1}^n f(x_i),\quad x_i\sim_{i.i.d.} X $$ What methods exist to ...
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Copula identification

I am looking a bivariate data and am trying to find a correct copula. I have been looking at the well known bivariate copulas (the archmedian copulas) but as I was looking, none of them seem to be the ...
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1answer
12 views

Statistical Test for Staffing Agency Selection of Employees

I am looking for the statistical test to measure the selection pattern from a pool of people. The staffing agency receives requests from a contract and then selects a person to fill the order. The ...
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1answer
27 views

Comparing linear regression models under violation of independence assumption

the basic setup is as follows: I have a continuous dependent variable (DV, 7 observations) and two continuous independent variables (IV1 & IV2). I would like to evaluate whether adding IV2 as ...
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2answers
31 views

Bounds of rain on both days on the weekend if events NOT independent

If $\mathbb{P}(\text{Rain on Sat}) = 0.5$ and $\mathbb{P}(\text{Rain on Sun}) = 0.3$. Then if independent, $\mathbb{P}(\text{Both Days}) = \mathbb{P}(\text{Rain on Sat}) \cdot \mathbb{P}(\text{Rain on ...
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On likelihood functions and characteristic functions

Let me preface this by saying that if someone manages to provide a solution to my problem, I will forever be indebted to them, as this problem has driven me crazy. Let us first assume that the ...
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22 views

Use both historical prices and fundamentals data for predicting portfolio profit?

Get highly accurate probability distribution for the future price of portfolio using all the data available. Each stock has two historical data - daily prices (scalar time series updated daily) and ...
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29 views

Robust sum of non-independent random variables

What approach could be used to sum non-independent variables? I have probability distributions of stock prices and want to calculate the probability distribution of the portfolio price (sum of some ...
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0answers
21 views

Analysing serial dependence in binary sequences

Suppose, I have a generator of a binary time series $x_t$. The generator produces a $1$ with probability $q$, except when there was a previous trial and the previous trial was a $1$: in this case the ...
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1answer
35 views

Non-Parametric statistical test for non independent repeated measure discrete data

I am working with a dataset the table form of which is as follows ...
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1answer
55 views

A simple question regarding AR(1) process and CDFs

Somewhat a trivial question, but I struggle to get my head around it. Consider we have an AR(1) process, as follows: $y_t=\rho y_{t-1}+\varepsilon_t,\quad t=1,...,T$. such that $\varepsilon_t$ are $...
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38 views

Does random forest (and, decision tree) require an independent observation assumption? [duplicate]

I am wondering if random forest models require an independent observation assumption. My date includes observations from the same participants, but I do not have a way to identify each participant. ...
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1answer
23 views

Order dependencies between binary variables

I have a series of random, binary variables that are sampled in a particular order. Some may be affected by the order in which they're sampled, i.e. there may be order dependencies. Suppose I sample ...
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0answers
19 views

Slight confusion on independent vs dependent samples

If I have two patient populations with cancer and I'm comparing cancer sizes, so say cancer size 1, 2 and 3 in an ordered fashion. Would these samples be dependent or independent? In one way, these ...
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3answers
777 views

Proof that if covariance is zero then there is no linear relationship

I get that a zero covariance doesn´t imply independence, but everybody says that if there is dependence and the covariance is zero then it is a non linear dependence. People base their interpretation ...
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1answer
102 views

Maximum Likelihood with dependent observations

In the context of a normally distributed dependent variable, the likelihood for a single observation is given as: $L(y_i|x,β,σ2)=\displaystyle\cfrac{1}{√2πσ^2}e^{\displaystyle\cfrac{(y_i−x_iβ)}{2σ^2}}...
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1answer
38 views

Probability of getting a 6 on at least one die from a pair of dependent dice

I am stuck on this particular question: Suppose you have two dice. These dice however are not independent: the probability that both dice will roll a 6 is 0.29. What is the probability that at least ...
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Multiple non-independent tests, how to determine post-test odds

Let's say a patient receives two biomarker tests to help with diagnosis of a disease. Each test measures a different mechanism of the disease, but these two mechanisms are not independent, so the ...

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