Questions tagged [compositional-data]

Refers to variables representing fractions of a total, i.e. all lying in $[0,1]$ interval and necessarily summing to one. Analysis of such data is often called compositional data analysis.

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neural network estimation of compositions distribution

To use feed forward neural network to predict compositional distribution, e.g.fractions of nutritions, vitamin 10%, protein 35%, water 35%, salt 20%, for each composition sample, sum composition ...
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Calculating distance with compositional and non-compositional data

I have demographic data across different districts/neighbourhoods, and would like to find, for a given district, which is its most similar peer district across multiple variables such as size (total ...
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Modeling probability mass over time for prediction

Consider a discrete random variable $X$ with three possible realizations $x_1,x_2,x_3$. This variable is observed over time, with the number of observations per point in time varying. The top ...
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power calculation for cox proportional hazard regression

I am trying to perform a statistical power calculation for cox regression. we want to investigate the association of composition (that has 4 variables) and sickness absence events in the future. for ...
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What to do when predictors are proportions that sum up to one?

I have a situation as the one described in the links below: Interpreting proportions that sum to one as independent variables in linear regression Predictor variables sum up to 1 but not necessarily ...
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Regression model not fully ranked

I am running a linear regression model with about 5000 cases. The dependent variable is income at closure an interval variable. I have run this model without problem many times. Now I am adding 9 new ...
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survival probability to proportional hazard ratios in r

I am using Cox proportional hazard regression to determine the association between physical behaviors (physical activity, sedentary behavior, and sleep) and mortality. to elaborate on these results, I ...
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Analyze categorical data when there cannot be “negative” influence

Suppose there are 1000 items given 5 labels [A,B,C,D,E]. You observe [750,200,25,25,0]. You want to find out whether items are biased towards being given certain labels. In a standard chi-squared ...
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115 views

Predict a vector of values with constraints? [duplicate]

I am aware of a variety of methods for simultaneously predicting multiple outcomes known sometimes as multivariate regression/analysis. However, my situation is a little more special. I am trying to ...
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109 views

What is the most appropriate transformation method for performing analyses on species composition data?

I would like to compare differences in fish diets between sampling sites using a Bray-Curtis dissimilarity matrix and non-metric multidimensional scaling techniques. My raw data consists of counts of ...
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Permutation testing for simulated compositional data

I'm testing some methods for estimating correlation in compositional data. As part of this process, I'm using the following approach: simulate un-normalized features $Y$ normalize features for each ...
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What type of chart is this? A crossing stacked area chart?

The New York Times made some beautiful visualizations of energy consumption by state: link What would this type of chart be called? A cross-stacked area chart? Does anyone know any libraries or ...
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Peanut butter jars full of river mud and bacteria?

I'm an environmental scientist looking into dynamics of bacteria growth in river bed sediments. I collected lots of data, and used regression for most of the comparisons, but one (the most important) ...
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Adding covariates to a log-ratio transformation

Let us say I am interested in predicting the evolution of market shares over time with a model that includes not only past lags of the variable, but also some covariates that are non-compositional, as ...
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233 views

Compositional Data and Machine Learning

One of my features is compositional of nature, represented by a vector [p1, p2, p3]. Each vector represents an emotion and each vector sums up to unity. Eg: ...
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153 views

Log-transformation of Compositional Data

I am dealing with compositional data, in a high dimension. Each sample I have behaves like: $$ {S}^D=\left\{\mathbf{x}=[x_1,x_2,\dots,x_D]\in\mathbb{R}^D \,\left|\, x_i>0,i=1,2,\dots,D; \sum_{i=1}...
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Correlation of Vectors with Constrained Sum

Taking the correlation of vectors with a constrained, fixed sum (say, a simplex, where sum is always 1) will induce spurious negative correlations, since increasing one element always means decreasing ...
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How do I model whether compositional data changes over time? [duplicate]

I have a data set of diet proportions over time (this is just a sample): ...
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257 views

Modelling Time Series of percentages

I am trying to model a multivariate time series of percentages. And here's the kicker, at each point, each of my individual time series are bound between 0 and 1, and their Sum per period equals 1. An ...
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274 views

Why robust PCA results change with each run?

According to Filzmoser et al. 2009, the best way to conduct a principal component analysis for compositional data with outliers is: using a robust PCA method and using the isometric log ratio ...
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Multiple Imputation of Mutually Dependent Data

I'm trying to construct summary variables for proportion of time spent in different employment statuses over an individual's working life (e.g. % of time spent unemployed between ages 18-21). My ...
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Classifying compositional vectors of time series

I am interested in classifying vectors of time series $x_t=(x_{1,t},\ldots,x_{n,t})$. In addition these vectors are subject to the restrictions $\forall i,t$: $0 \leq x_{i,t} \leq 1$ and $\forall t$: $...
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Dirichlet regression using jags [closed]

I am trying to fit a simple Dirichlet regression using rjags with a parametrization in terms of the mean and the precision. The model is written as follows: model { # (0) priors for (i in 1:(...
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Comparing observed and expected diets of two different species

My data consists of dietary data from two species (C1 and C2) and expected diets for each species (E1, E2) generated from a combination of variables, but is based on their foraging behavior. What I ...
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Is this usage correct for using isometric log ratio [ILR] transform with counts data (compositional)?

If one wanted to construct a simple pairwise correlation matrix from an compositional data table using an ILR transform preprocessing step, would this usage violate any assumptions with the transform? ...
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Forecasting proportions of aggregations vs direct forecasting

Assume one has to predict the sales of a shop on a daily basis. The sales per day $S(t)$ clearly follow a strong weekly pattern, but also a yearly pattern, a general trend and of course some noise are ...
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224 views

Can compositional data (percentages) be used in the explanatory data matrix of an RDA or CCA?

I would like to know if compositional data (percentage) can be used in the explanatory data matrix of a redundancy analysis (RDA) or canonical correspondance analysis (CCA) (not to be confused with ...
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242 views

Interrupted Time Series Segmented Regression for Rates

I would like to test an intervention using interrupted time series (segmented regression). I have monthly rate (proportion) data with many of the rates in the <0.10 range. Should I use a standard ...
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Help with interpretation of output

I am running a model in which I want to explain my dependent variable with the racial/ethnic diversity in a person's residential area. Diversity is measured with 4 continuous variables. Each one of ...
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110 views

Logistic transform of multivariate zero-mean Gaussian

Consider a multivariate logistic-normal variable $z \sim \mathcal {LN}(\mu,{\Sigma})$, where ${\Sigma}$ is and $n$-by-$n$ positive definite matrix. I mean, for $x = (x_1,\ldots,x_n)\sim \mathcal N(\mu,...
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165 views

PCA for probability vectors

Is there a procedure equivalent to principal component analysis (PCA) for probability vectors? I have an n-by-m array where every column sums to one, and all entries are positive. PCA works in ...
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276 views

Clustering vectors which values are probabilities (summing to 1)

I have an n-by-m array, where every column sums to 1, in other words I have m probability vectors of size n. I would like to cluster them into several categories. I will appreciate, if somebody ...
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Can I use the CLR (centered log-ratio transformation) to prepare data for PCA?

I am using a script. It is for core records. I have a dataframe which shows the different elemental compositions in the columns over a given depth (in the first column). I want to perform a PCA with ...
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177 views

Can I use proportions as continuous independent variables in a regression?

I was assuming I can until I come across the concept of compositional data. Now I'm confused. My DV is a binary outcome, my IVs are proportions, say: A, B, C where A+B+C=1. I was going to run a ...
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711 views

Interpretation of the Precision Model in Dirichlet regression

I use dirichlet regression to analyze the result of a membership matrix (compositional data). For each observation, I have membership probabilities to different groups and these probabilities sum to ...
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How would you analyse dependence of proportions?

We are given a compositional data set, where the response is $$Y = [y_1, ..., y_n], \sum y_i = 1, y_i \in [0,1]$$ I intend to do regression, however, prior to that, I would like to get a feel of the ...
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691 views

Ternary diagrams in scatter plot matrix (pairs) with R “compositions”

In the documentation for the R compositions package, and in reference to ternary diagrams, it is stated that: However the ternary diagram can only display ...
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Is this a multivariate regression problem or separate univariate regression problem?

I have data on the percentage of their 24h day that animals spend doing certain activies. One response for one animal may look like 30 % spent hunting 30 % spent sleeping 30 % spent eating 10 % ...
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Interpretation of inverse ILR-transformed coefficients from a compositional data analysis

I wish to do regression analysis on compositional data. But whatever I've learnt from books and blogs that I need to use transformations like centered log ratio (clr...
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What should be rank of matrix with compositional data variables?

I'm doing compositional data analysis on 'Baysite' dataset under 'compositions' package in r. Aim is to find nature of the relationship of its permeability to the mix of its four ingredients: A: ...
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246 views

Why is compositional data not analyzed using anova?

Compositional data looks like this: $[p_1, ...., p_n]$ where $\sum p_i = 1$. My question is, I know that we can analyze this using log-ratio analysis but ... Why not just use anova? Take each of ...
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Is the normal linear model analysis “rotation-invariant”? On alr vs ilr

Abstractly speaking, are the methods of regression and analysis of variance in normal linear models, along with hypothesis tests and confidence intervals, etc., "rotation-invariant"? In particular, ...
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How do you interpret parameters from logratio analysis of compositional data?

In compositional data analysis as studied by John Aitchison, the analogue of simple linear regression is $$Y_i = \alpha\oplus\beta\odot X_i \oplus \epsilon_i$$ Here, $Y_i = [y_1,...,y_n]$ is the ...
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327 views

Compositional data analysis - what's the “method”?

Let $\textbf{X} = (X_1, \ldots, X_n)$ be a vector of responses, where $X_i = (p_1, \ldots, p_k)$ is itself a vector of probabilities. What method does one use to analyze such data? I want the logic/...
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332 views

Overview of compositional data analysis

I just need a very short summary of what the standard way to deal with compositional data is. I've skimmed pages in a 500-page long book on the topic, and I didn't really gather much. I would like ...
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Applied logratio analysis. Where do you learn it?

I want to analyze compositional data using R. Dirichlet regression has been proposed, but the logratio analysis methods seem to constitute a more complete and well-tested approach, so I want to learn ...
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What are the differences between Dirichlet regression and log-ratio analysis?

Compositional data can be analyzed by either Dirichlet regression or using log-ratio analysis as pioneered by John Aitchison. My questions are What are the main differences in assumptions between ...
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How can I check if my data follows a Dirichlet distribution?

I have some compositional data, and I intend on using log ratio analysis. However, if my data could be modelled to be Dirichlet distributed, then that might be a more preferable approach. But how do I ...
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Are there potential pitfals to compositional data with many components?

I currently have a data set where the response is compositional with many components. I am considering lumping some of the components together. I believe this will make it easier to spot the ...
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Why can't I just analyse compositional data using regular multivariate analysis?

For a data set, I have compositional response variables: probabilities that sum to 1 Why can't I just analyse this using a linear model or alternatively, say, a generalized linear model, where I use ...