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It is a set of statistical methods that aims to evaluate multivariate data sets simultaneously in the sense that there are several measured variables for each specific or object considered. The reason for its existence is an improved understanding of the phenomena under learning, and to obtain facts that statistical methods and bifurcated statistical methods cannot be obtained.
Objectives of Multivariate Analysis can be synthesized in two:
1) Provide methods whose purpose is the joint study of multivariate data that one-dimensional and two-dimensional statistical analysis is inept to attain.
2) Help the analyst or investigator to make optimal decisions in the situation in which they are, taking into account the evidence available from the evaluated data set.
They can be classified into three large groups:
1) Dependency methods- They accept that the analyzed variables are distributed into two groups: one is the dependent variables and the other is independent variables. The purpose of dependency methods is to conclude whether and in what way the set of independent variables have an impact on the set of dependent variables. They can be classified into two large subgroups according to whether the dependent variables are qualitative or quantitative.
The condition when the dependent variable is quantitative, some of the techniques that can be applied are the following:
2) Methods of interdependence- These approaches do not discriminate between dependent and independent variables and their purpose is to recognize which variables are interrelated, how they are related, and why. They can be categorized into two large groups according to whether the type of data they analyze is non-metric or metric.
In case the data is metric, the following techniques can be used, among others:
Its objective is to classify a sample of entities in a small number of groups so that the interpretations belonging to a collection are very similar to each other and very dissimilar to the rest. Unlike the Discriminant Analysis, the number and structure of these groups are unidentified.
If the data is non-metric, the following techniques can be used, in addition to Multidimensional Scales and Cluster Analysis:
3) Structural methods- They assume that the variables are distributed into two clusters: that of the dependent variables and that of the autonomous ones. The objective of these methods is to analyze not only how the independent variables make an impact on the dependent variables, but also how the variables of the two clusters are related to each other.
They analyze the relationships between groups of variables represented by systems of simultaneous equations in which it is assumed that some of them (called constructs) are measured with error from other observable variables called indicators.
The models used therefore consist of two parts: a structural model that specifies the dependency relationships existing between latent constructs and a measurement model that specifies how the indicators are related to their corresponding constructs.
1) Objectives of the analysis- The problem is defined by specifying the objectives and the multivariate techniques to be used
The researcher must establish the problem in conceptual terms by defining the fundamental concepts and relationships to be investigated. It must be established whether these relationships are going to be relationships of dependency or interdependence. With all this, the variables to be observed are determined.
2) Analysis design - The sample size, the equivalences to be estimated (if applicable), the distances to be calculated and the approximation techniques to be used are determined. After all, this is determined, the data is observed
3) Analysis hypothesis-The hypotheses underlying the multivariate technique are evaluated. Said hypotheses can be of normality, linearity, independence, homoscedasticity, etc. You must also choose what to do with the missing statistics.
4) Carrying out the analysis- The model is estimated and the fit to the data is evaluated. In this step, atypical or influential observations (outliers) may appear whose effect on the estimates and the truthfulness of appropriation must be analyzed.
5) Interpretation of results- Such analyses can lead to extra re-specification of the variables or the model, which can return to steps three and four.
6) Validation of the analysis- It consists of establishing the cogency of the results obtained by scrutinizing whether the results obtained with the sample are widespread to the population from which it moves toward. For this, the sample can be divided into several parts in which the model is re-estimated and the results compared.
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