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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15 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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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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18 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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29 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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33 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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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
20 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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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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523 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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76 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
26 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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Distribution of the squared norm of a vector with multivariate normal distribution and dependent components [duplicate]

Let x be a p-dimensional random vector with dependent components. Assume that x is distributed according to a multivariate normal distribution with mean vector m and variance/covariance matrix V which ...
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1answer
37 views

Statistical significance testing when distributions are paired, but samples are not

I have a situation like the following: 5 distributions A, B, C, D, E of unknown type from which I can take samples to estimate the mean. I apply an intervention or treatment to all of the ...
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79 views

Characteristic function of $X+X^2$ if $X$ is a standard Gaussian random variable

Can anyone please tell me how I can find the characteristic function of the random variable given by the sum $X+X^2$ where $X$ is a standard Gaussian random variable? Many thanks!
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chi-square when the cells are not independent

Imagine an experimental setup as follows: 30 subjects each make three preference judgements: they choose a color for each button shape. So, the raw subject data could look like: ...
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Means centralization, is it a thing?

Assume a dataset of counts in distances (1, 2, 5, and 10) to a point from three independent samples (a, f, and ...
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Can I do a regression with 3 independent observations and inside of each several nested (thus dependent) observations?

I have an (ecological/soil science) experiment with a multiple nested design with 3 real independent observations (sites with different caracteristics), and several dependent observations within them (...
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LMM: Non-independence of observations sharing a single fixed-effect value

I am interested in the effect of monkey's stress levels on the pitch of their calls. Each stress measurement is associated with a bout of calling (that is, multiple calls), and in some cases I have ...
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Violation of Independence of Observations - Logistic Regression

Apologies if this seems a basic question but I can't find enough detailed information about what exactly constitutes a violation of independent observations. The regression I'm wanting to run is ...
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1answer
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How to test mean differences in proportions that are dependent

I have an experimental setup where I have allowed groups consisting of about 50 animals to select between two environmental conditions. I.e. animals had the possibility to move between the two ...
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1answer
107 views

Comparing Spearman rank correlations between many dependent lists

I have a list of values $S$. I want to compare the Spearman correlations of $S$ with $N$ other lists of values $O_k$ ( $k∈[N]$ ). The lists $O_k$ are not independent. Each value $O_k^j$ ( $j∈[|O_k|]$ )...
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Treating dependent timepoints as independent

I've been given a data set to work with that includes measurements of the same group of individuals over approximately 6 months (3 measurements total). The problem is that they did not include any ...
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Sign of Covariance and of Spearman's Rho

Has anybody available a proof that the covariance between two variables has always the same sign as Spearman's Rho, assuming that both are not zero, or an explanation / counterexample to show why this ...
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Dependent variables, regression

I am trying do make some descriptive statistic. In my dataset I have ID, Age, time from start of being registered, sex, birth-place. The time from start of being registered minus date 15 June 2019 ...
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Is an autoregressive model considered a model for independent or dependent data?

It seems to me that, in the statistical literature, data, models, and inference seem to conflate the terminology of dependent and independent. Case 1: a cross sectional sample of weight and height ...
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268 views

Is there a way to cluster data using a dependent variable? [closed]

We are conducting research on neighborhood mail response behavior, i.e. what percentage of people in a neighborhood reply to a piece of mail. Based on regression analysis, we know which factors (% ...
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Repeated measures/pseudoreplication - Comparing all samples against all other samples

I am currently analysing some data, and I am not confident that I am going about it in as statistically sound way. We are trying to determine whether our treatments affect the distance between two ...
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How to deal with subset of variables that are invariant for subsets of sample

I am thinking about a problem in which I have a sample which consists of subsamples with the same values for a subsample of independent variables. I want to apply a simple linear regression with ...
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33 views

Test to compare means of non independent samples with repeated measures

I am struggling a little to know if I am comparing independent or not independent data and I am not sure what kind of test I should use. Here is the pitch : I would like to compare latencies between ...
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21 views

Extract covariate adjusted dependent variable from linear regression model?

I want to adjust a continuous (dependent) variable for two independent variables (1 categorical, 1 continuous) and then use the residuals + intercept for plotting by another categorical variable. Is ...
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15 views

Use of a predictor variable for a dependent variable that is directly related to the predictor variable

If I would like to predict a binary variable x, and x is true if y is true and ...
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1answer
36 views

Correct C-Vine Configuration to emulate a predefined correlation matrix

I am trying to simulate a vine copula with a predefined dependence structure, so I can generate samples for my desired dependence structure. However, I am having trouble defining the Vine structure ...
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1answer
45 views

Alternative to GLM with non-independant observation

I would like to perform a regression to study association between 3 categorical variables and a presence/absence response variable. I was planning on using a GLM. However, my observation unit being ...
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Confused about multilevel analysis and non independence of observations

I'm still struggling with my understanding of multilevel analysis, wondering if it applies or not to my problem. I'v read here the following (where author gives an example of a multilevel model with ...
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When does $E[f(X_i)]=E[f(X_j)], i\neq j$?

Suppose we have random variables $X_1, \dots, X_N$, with joint probability distribution $F_{X_1,\dots,X_N}$. Under what conditions does the following equality holds? $$E[f(X_i)]=E[f(X_j)],\ \ i\neq ...
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Clustering items based on response behavior on three tasks

I have a question and was hoping someone could point me in an appropriate direction. I conducted a large experiment and would now like to find patterns in the response behavior of the subjects. The ...
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how to handle non-independent experimental data

I have data to analyse that involves 12 treatments. Each treatment was "replicated" 3 times, for 36 observations. But the experiment involved applying the treatment to 1 side of an object -- and most ...
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How to test the equality of two Pearson correlation coefficients computed from the same sample?

Is there a reliable way to say if two Pearson correlations from the same sample (do not) differ significantly? More concrete, I calculated the correlation between a total score on a questionnaire and ...
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1answer
32 views

Estimation of model with non linear dependent variable

I am trying to verify whether two variables are linked by a relation of the type: |y|=ax or y^2=ax. What could be the right statistical procedure to verify whether the above relations are correct and ...
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Why dependencies would cancel while paramterizing CPD?

Consider that in CPTs of a Bayes Net(structure is fixed) one dependence is fix(parameters are set for $P(X|Y)$) and we are parameterizing other CPDs, is it possible that the other parameters would ...
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Regression with dependent data with low dependence

Suppose you have data that is grouped in one way or another and therefore the assumption of independence is suspect. But you look at the intraclass correlation (or autocorrelation) and it is very ...
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2answers
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Can statistical dependence arise only at the limit?

(This has been inspired by a comment exchange with @guy). Assume we have two infinite sequences of random variables, $\{X_n\}$ and $\{Y_n\}$. Assume the RVs in $\{X_n\}$ are statistically ...
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Compare categorical variables that are not(?) independent

I have some survey data in which respondents were classified in to two overlapping groups (i.e. respondents who work in a profession and people who do this same work on their own-- many people do ...
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Which test to run for effect of nominal independent variable on multiple ordinal dependent variables

Im new to stats so dont shoot me. I am trying to work out what is the correct test to run in the following scenario Does the independent nominal variable of colour, with four categories (Blue, Brown, ...
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statistics of (possibly) non-independent interacting systems with fat tails

I apologize if this question has already been asked. I don't know the proper terminology to find my answer - so if it has, please direct me to it! Problem setup: I have many time series of a ...
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Can two variables be included in same model when if binary B=0, continuous C>0 and when B=1, C=0?

I am interested in looking at the effect of both a binary predictor ("B") and a continuous predictor ("C") on an outcome. However, the value of C is conditional on B in that for B=1, C=0; for B=0, C>0....
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Standardised effect size and CI for non-independent longitudinal data in a linear mixed-effect model (LMM)

I would like to calculate standardised effect sizes with confidence intervals for fixed effects in a linear mixed effect model (LMM) for data that have an unbalanced repeated measures longitudinal ...
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1answer
63 views

Govt. organisation favouritism in its complaint handling

I am analysing some data for a government organisation and trying to convince them that their complaint decisions are biased. I believe they favour certain organisations. I have put together the ...
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Two correlated ordinal independent variables, several continuous dependent variables

I am currently struggling with a somewhat atypical analysis. People have been evaluating their cognitive state at two time periods – when they had attended school and at the present moment. Naturally, ...