How to create a dependent variabel using a number of different independent variables?

I have a data that consists of number of different independent variables (no dependent variable), whose values are observed at different time points.

I need to find a new dependent variable that is dependent on these independent variables, so that I can use that to compare different data sets containing similar data.

How can I do that? And is there some mathematical/statistical score that can be used as a dependent variable.

Thanks

Answer 1

[TED MOSBY]

Hi,

You can think of creating a dependent variable from your set of independent‐only time series as an unsupervised dimensionality-reduction problem. The workaround for that is Principal Component Analysis (PCA). The first principal component is a linear combination of your original variables that explains the maximum possible variance, and its score time series makes a natural “new dependent variable” you can compare across data‐sets:

% Suppose your data is in a TxN matrix X, where:
%  T = number of time points
%  N = number of “independent” variables measured at each time

% Standardize each column to zero‐mean, unit‐variance
Xz = zscore(X);

% Run PCA:
%    coeff  = N×N matrix whose columns are principal directions (loadings)
%    score  = T×N matrix whose columns are the principal‐component time‐series
%    latent = N×1 vector of variances explained by each component
%    explained = N×1 percent of total variance explained
[coeff, score, latent, ~, explained] = pca(Xz);

% (3) Your “new dependent variable” = the first PC’s scores
newY = score(:,1);

Refer to these links for more information on "pca" and "zscore" :

https://www.mathworks.com/help/stats/pca.html?s_tid=srchtitle_support_results_1_pca#bth9ibe-score

https://www.mathworks.com/help/stats/zscore.html?s_tid=srchtitle_support_results_1_zscore