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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How to perform isometric log-ratio transformation
I have data on movement behaviours (time spent sleeping, sedentary, and doing physical activity) that sums to approximately 24 (as in hours per day). I want to create a variable that captures the ...
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Do I need to drop variables that are correlated/collinear before running kmeans?
I am running kmeans to identify clusters of customers. I have approximately 100 variables to identify clusters. Each of these variables represent the % of spend by a customer on a category. So, if I ...
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Clustering of very skewed, count data: any suggestions to go about (transform etc)?
Basic problem
Here is my basic problem: I am trying to cluster a dataset containing some very skewed variables with counts. The variables contain many zeros and are therefore not very informative for ...
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What are some distributions over the probability simplex?
Let $\Delta_{K}$ be the probability simplex of dimension $K-1$, i.e. $x \in \Delta_{K}$ is such that $x_i \ge 0$ and $\sum_i x_i = 1$.
What distributions which are frequently (or well-known, or ...
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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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What test to compare community composition?
Hope this newbie question is the right question for this site:
Suppose I would like to compare the composition of ecological communities at two sites A, B. I know all three sites have dogs, cats, ...
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Why is it not OK to do a Pearson correlation on proportion data?
An online module I am studying states that one should never use Pearson correlation with proportion data. Why not?
Or, if it is sometimes OK or always OK, why?
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Why is isometric log-ratio transformation preferred over the additive(alr) or centered(clr) with compositional data?
I'm doing linear regression on compositional data using log-ratio transformation with census data. The IVs are compositional (percents summing to 100). The DV is non-compositional and continuous.
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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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Problems with time series prediction
I got a question about modeling time series in R.
my data consist of the following matrix:
...
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Distributions on the simplex with correlated components
I'm looking for some kind of distribution over the simplex in which components are correlated in an ordinal way. That is, if $p = (p_1, ..., p_J)$ is drawn from our distribution on the simplex, I ...
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How to use isometric logratio ilr() from a package "compositions"
I have an environmental dataset, where observations do not sum up to 1.
I suspect that data are a subcomposition, meaning that not all elements have been measured and that is why observations do not ...
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Multivariate proportional data
I am looking for literature on what I call multivariate proportional data where a single observation is a vector of proportions that sum to 1. For example, each person weights their preferences for ...
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Can I use logistic regression when all of the regressors sum to 1?
Let's say I want to perform a logistic regression (binomial) as :
X ~ P1 + P2 + P3 + P4 + P5
where X is binary variable (0 or 1) and P1, P2, P3, P4, P5 are ...
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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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Multivariate data analyis of compositional data
Suppose I have a multivariate, compositional dataset that depicts the concentration of different elements. However, the data are not available on a single scale; i.e., some are of form 0.00x while ...
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Predicting proportions with Machine Learning
I am working on a machine learning problem where I have to predict a set of $N$ numbers (proportions) for each data point, all of them summing to one. One toy example to illustrate my problem would be ...
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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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Overall $p$-value for a multiple linear regression (in MATLAB)?
I wish to explore the effects of the component percentages (independent variables) on fruit sweetness $S$ (dependent variable). Assume for simplicity that our fruit only contains 3 components, ...
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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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How to test over-dispersion for a compositional data in R?
I would do an over-dispersion test for a compositional data set (I don't have the original count values) for choosing later an appropriate regression model. Here is an example of my data set:
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Possible classification techniques to use when each feature is a probability distribution
I am working with some data where the features have a temporal aspect (e.g. how often does a feature occur between $t_{begin}$ and $t_{end}$). I am trying to build a binary classifier for this data. ...
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Log-Ratio \ Compositional analysis
I am not a trained statistician but I am trying to improve on my own MBA thesis which was essentially regression analysis of the factors affecting opening cinema box-office in the UK.
I am now ...
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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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Analysing data measured as proportional composition
I have a data set on the proportional composition of marine substrate for different locations which I would like to compare. For example, one replicate transect within a location may be 50% sand, 25% ...
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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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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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Combination of correlations: How to correlate compositions?
How to correlate a set of compositions to a same-sized set of estimates of these compositions?
-> composition(estimated) vs composition(real)
Imagine you have a mixture of 5 liquids A+B+C+D+E, ...
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Visualizing composititional time series with negative values and meaningful totals
I have a compositional time series containing negative values, like this:
...
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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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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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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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R - multinomial logistic regression with relative frequencies as response variable
My colleagues observed in an experiment involving categorical and continuous independent variables, how the species composition changes. Approximately equal numbers of microbes were used in the ...
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Compositional Data in R
I'm writing a work on the Aitchison geometry for compositional data and I have seen an Image I want to reproduce in R.
I work with the "compositions" library and I want to understand how to ...
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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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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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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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Non-logarithmic approaches to compositional data
Background
Compositional data ($x_i>0, \sum_i x_i=c$) are usually analyzed using some kind of log-transformation (alr/clr/ilr), to take into account naturally the fact that, in presence of the sum ...
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Finding mean and SD of 2 parts of a whole
I am putting together a review/meta-analysis of body composition in children. The data I will analyze consists of measures of fat-mass (FM) and fat-free-mass (FFM), which when summed equal total mass....
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Standardization of compositional data in PCA versus using real data
I have a question about conducting a PCA between variables that are measured in different units. I understand the importance of using a correlation matrix versus a covariance matrix to minimize ...
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How do I compare explanatory power of Dirichlet regression with other models?
I have a dataset with 7 variables expressed in % of the total (i.e. one of the constraints is that sum of the variables = 100%).
I am looking at Dirichlet regression in R for the first time (I am ...
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Best way to analyse percentage data
I have percentage data and would like to see if these different variables have an affect on certain factors;
i.e., I have different habitats of an area e.g., improved grassland: 40%, arable: 15%, ...
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Models that force regression predictions to sum to 100?
I have a dataset with some covariates and a response variable which is a composition of 3 classes (A,B,C).
For example, in the observed data: Person 1 (80% A , 15 % B , 5% C), Person 2 (50% A, 20% B, ...
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How does removal of symmetry (e.g. via constraints) in a Bayesian optimization search space affect search efficiency?
There are many examples of search space symmetry in real-world optimization problems in the physical sciences. To motivate this, here are some that come to mind:
When optimizing a formulation such as ...
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Compositional Data Analysis: What is the connection between Soft-max Regression / Logistic Regression and Linear Regression in the Simplex Space?
As someone just learning Compositional Data Analysis, my understanding is the following:
The sample space for Compositional Data Analysis is the Simplex Space. Useful transformations like ALR/ILR/CLR ...
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Machine Learning Classification with Variables Summing to One
Suppose you have data with a bunch of predictors, and some of these predictors are proportions that add up to one. An example would be data like the following
...
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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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Dirichlet regression with repeated measures
My dependent variable is composition (proportions of a whole object), so I have found that a Dirichlet Regression would be a potential option. However, my study collects repeated measures. Can this ...
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