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Principal component analysis (PCA) is a mathematical procedure that uses an orthogonal transformation to convert observations with correlated values that compromise uncorrelated variables known as principal components. The first principle is getting the highest variance. The principal component analysis concept was coined in 1901 by Karl Pearson. It is used to cut down large sets of variables into smaller sets containing all the important information available in the large sets.
Objectives if Principal component analysis
• The main aim of PCA is to reduce data dimensions without the assurance that the dimensions will be interpretable.
• It cuts down the attribute space from a large number of variables to a small number of variables using a non-dependable procedure.
• It makes it easy to pick a subset of variables from an extensive set of variables depending on the original variables with the highest number of correlations with the principal component.
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Applications of the nonlinear mixed effect models
1. It is used to model the progression of a disease
2. Modeling the cognitive decline in Alzheimer’s disease
3. It is used as a model for estimating the means curves of human weight and height
4. For population pharmacokinetic modeling, etc.
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Incorporating covariates is a good way of building flexible nonstationary covariate models. In statistics, covariate and response data are often involved in misaligned data in space. A common strategy is applied to interpolate the covariate in the locations with response data to avoid bias parameter estimation and prediction. Both response and covariate processes are represented in a basic system, and the covariate effect is introduced through a linear model between the coefficients of the basis vectors.