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Multivariate Statistics

Multivariate statistics is mainly concerned with the study of evaluating multiple variables concurrently and analyzing the effect of each variable. It provides a way to differentiate the effect of each variable in a statistics model. It analyzes the data of different types of observation with the help of statistical procedure.

With the involvement of multiple probability distribution, it can be used to signifies the distribution of the evaluated data. It also deals with the various concepts viz. Bonferroni Method, Clustering Systems, Confirmatory Factor Analysis, Factor Solutions, Fisher’s Approach, Likelihood Function, Linear Discriminant Analysis, Monte Carlo Simulation, Multiple Coefficient of Determination, Partial Least Squares, etc.

Major software that involved in the Multivariate statistics field:

  • R software
  • SAS software
  • SPSS software
  • STATA software

Multivariate Statistical analysis plays an important role in the social science research. In this field, Multivariate Statistical analysis enables Researchers to use the randomized laboratory experiments in the natural science and in medicine. Some of the researchers take the help of quasi-experimental designs, but with this, these is some differences occurs in the starting stage that affect the output of the study. Multivariate techniques try to overcome the differences and to adjust the output.

Multivariate Methods comprises of cluster analysis, factor analysis and related concepts. It is modern concept of Statistics that defines the techniques for analyzing the individual variables concurrently. It also describes the method which provides the perception into the structure of multivariate data.

Factor analysis is a type of multivariate statistical evaluation which used to define the collection of detected variables. It used to observing variable relationships for some major concepts which including dietary patterns, psychological scales and socioeconomic status. Main objective of factor analysis is to mitigate the variables and to acquire the sensible explanation of the detected variables by factors. A user can used factor analysis to interpret the structure and underlying patterns in data. Factor analysis also used in the hypothesis testing, data transformation, pattern delineation, etc.

Moreover, Multiple Analysis of Variance mainly concerned with the ANOVA to cover the instances where there are several variable exists to be examined simultaneously. ANOVA is a one-way analysis of variance whereas MANOVA is a two-way analysis of variance. It is used to analyze the more than one dependent variable and to compare the multivariate sample. It tells us about the effect of the changes in independent variables on the dependent variables, relation between the dependent variables and relationship between the independent variables. It works with the assumption that dependent variables are continuous variables and independent variables are categorical variables.

Regression analysis is defined as a statistical process that assembles the more than one predictor variables which leads to a resultant variable. The resultant can be either dichotomous or continuous. If the resultant variable is dichotomous then it is known as logistic regression. Researchers mainly used the regression analysis in order to estimate the social and economic happenings.

Multivariate analysis deals with the examination that is made on many variables. Main aim of Multivariate analysis is to know about the relationship between the variables. It is used to represent the distributions of the examined data in the context of Probability distributions. It is used for solving the problem where there is one dependent variable is analyzed by the other variable simultaneously. There are two types of variables take place in the Multivariate Analysis, including Dependent variable and Predictor variable. Some of the uses of the Multivariate analysis are as follows:

  • Capacity based layout
  • Inverse layout
  • Analysis of Alternatives
  • Assessment of theories
  • Recognition of layout

Sparse regression model describes the meaning of sparse. Let us assume a situation: when number of signal dimension (pp) is more than the number of samples (nn) then this situation is termed as regression model.

SparseReg toolbox comprises of MATLAB functions which is used for the saprse regressions. Sparsity deals with the polynomial trend filtering, variable selection, variation regularization, etc. Various types of penalities that implemented in this are:

  • Log penalty
  • Elastic net
  • Power family
  • SCAD and MCP

Bayesian approaches are based on the probability. It is consistent and provides the best reflection of scientific reasoning. Bayesian inference is the one of the most known Bayesian approach. Bayesian inference is the technique that plays an important role in the statistics. Application of Bayesian inferences is found in the various areas science, sport, law, engineering and philosophy.   It is also known as the Bayesian probability as it related to the field of probability.

Baye’s rule mainly concerned with the conditional probability. Bayes’ rule can be represented as:

P (H/E) = {P (E/H) . P (H)} / P (E)

Furthermore, Some of the major concepts that involved in the Multivariate statistics are Cochran Theorem, Canonical Variates, Canonical Correlation Analysis, K-Group Problem, Q Type Analysis, Wishart Distribution, RV coefficient, Strucutural Equation Model, Partial F Values, Multicollinearity, Logistic Discrimination, and many more.

Along with these concepts, few advance topics that mostly chooses by the PhD level students to make their thesis are:

  • Canonical Correlation Analysis
  • ANOVA
  • Mixed Effect Models
  • Multivariate modeling approaches
  • Nuclear norm regularization
  • Multidimensional Scaling
  • Covariance estimation and graphical modeling
  • Mixed Effects Logistic Regression Models

Whenever you want to write an assignment on Multivariate statistics, let us know. Our Multivariate statistics Experts are trustworthy and they provide the plagiarism free assignment on the all general and complex topics of Multivariate statistics, such as Logit Models, Mancova, Multidimensional Effect Patterns, Multivariate Normal Distribution, Ordinary Least Squares Approach, Two Group Discriminant Analysis, Recursive Portioning, Correlated Predictors, Latent Structure Analysis, and many more. With assignment, we provide you some wonderful services:

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Visualization
 
  • Principal component analysis, Multidimensional scaling, Exploratory factor analysis, Cluster analysis, Supervised learning, The multivariate Normal distribution, Canonical correlation analysis, Graphical models, Multivariate normal distribution, conditional densities, partial correlation, multiple correlation, regression coe , cients, maximum likelihood estimates, Hotelling's statistic
  • Wishart distribution, tests of hypotheses, linear discriminant function, matrix operations and random vectors, Numerical and graphical summaries of multivariate data, Multivariate normal distribution, Inference for multivariate mean, Comparison of two or more mean vectors, Multivariate Linear Regression, Principal Components, . Factor Analysis, Discrimination and Classi , cation, Cluster Analysis, Canonical Correlation
 
Multivariate Data
  • Descriptive Statistics, Rows (Multivariate Statisticss) vs. Columns (Variables), Covariances
  • Correlations and Distances, The Multivariate Normal Distribution, Scatterplots, More than 2 Variable Plots, Assessing Normality
 
Multivariate Normal Distribution, MANOVA, & Inference
 
  • Details of the Multivariate Normal Distribution, Wishart Distribution, Hotelling T2 Distribution
  • Multivariate Analysis of Variance (MANOVA), Hypothesis Tests on Covariances, Joint Confidence Intervals
 
Multidimensional Scaling & Correspondence Analysis
  • Principal Components, Correspondence Analysis
  • Multidimensional Scaling
 
Discriminant Analysis
  • Classification Problem, Population Covariances Known, Population Covariances Estimated
  • Fisher’s Linear Discriminant Function, Validation

Topics for Multivariate Statistics

  • Estimation and Hypothesis Testing for multivariate normal data, Principal Component Analysis , Factor Analysis, Discriminant Analysis, Cluster Analysis, Correspondence Analysis, Multivariate normal distribution, maximum likelihood estimation
  • Wisharts distribution, Hotellings T2, hypothesis testing , Principal Components Analysis , derivation of principal components, PCA structural model, PCA on normal populations, biplots, Factor Analysis orthogonal factor model, estimation and factor rotation., Linear discriminant analysis, Fisher method, discrimination with two groups, Hierarchical clustering methods, measures of distance
  • non-hierarchical methods, model-based clustering., Concepts of correspondence analysis, chi-square distance , inertia multiple correspondence analysis, Estimation methods, Multilevel modelling , matrix algebra for statistics, Principal components analysis , Factor analysis, structural equation modelling

 

statistics for multivariate data :
multivariate data visualization
multivariate Normal distributions
Principal Component Analysis :
geometric and algebraic of PCA
calculation and choice of components
plotting PCs
interpretation
Factor Analysis :
model definition and assumptions
estimation of loadings and communalities
choice of the number of factors
factor rotation
Canonical Correlation Analysis:
computation and interpretation
relationship with multiple regression
Discriminant Analysis and Classification:
classification rules
linear and quadratic discrimination
error rates
Cluster Analysis:
measure of similarity
hierarchical clustering
K-means clustering
model based clustering

Multivariate Data :
Descriptive Statistics
Rows vs. Columns
Covariances
Correlations and Distances
Multivariate Normal Distribution :
Scatterplots
Variable Plots
Assessing Normality
Multivariate Normal Distribution,MANOVA, & Inference :
Wishart Distribution
Hotelling T2 Distribution
Multivariate Analysis of Variance
Hypothesis Tests on Covariances
Joint Confidence Intervals
Multidimensional Scaling & Correspondence Analysis :
Principal Components
Correspondence Analysis
Multidimensional Scaling
Discriminant Analysis :
Classification Problem
Population Covariances Known
Population Covariances Estimated
Fisher’s Linear Discriminant Function
Validation

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