Multi Variate Analysis

Data set: Environmental Readings per Country

Ritesh Malaiya

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Overview

Dataset

• Data: Measurements of environment conditions in Countries
• Rows: There are 137 observations, 1 for each country.
• Columns: Total 29 variables
  • Qualitative: Country (nominal), Happiness (Ordinal).
  • Quantitative: Aspect, Slope Crop Land, Tree Canopy Wind Cloud & Multiple variables for Temp & Rain

Methods

Quantitative

• PCA

Qualitative

• MCA

• DiCA

Grouping variables to observe relative effect among groups

• PLS-C

• MFA

• Cluster Analysis (DiSTATIS)

Correlation Plot

Heat plot

Quantitative Analysis

PCA

Methods	Unhappy	Normal	Very Happy	Reliability
PCA	Others	Temp & Rain	N/A	Components have significant contribution but convex hull has overlapping areas and Component 2 & 7 contradicts

Qualitative Analysis

Data Binning

MCA

Methods	Unhappy	Normal	Very Happy	Reliability
PCA	Others	Temp & Rain	N/A	Components have significant contribution but convex hull has overlapping areas and Component 2 & 7 contradicts
MCA	warm summers, cold winters, high rain	N/A	Warm winter, cold summer, low rain	Components have significant contribution but convex hull has overlapping areas

MCA Inference

Discriminant Correspondence Analysis (DiCA)

Methods	Unhappy	Normal	Very Happy	Reliability
PCA	Others	Temp & Rain	N/A	Components have significant contribution but convex hull has overlapping areas and Component 2 & 7 contradicts
MCA	warm summers, cold winters, high rain	N/A	Warm winter, cold summer, low rain	Components have significant contribution but convex hull has overlapping areas
DiCA	warm summers, cold winters, high rain	Higher variation in temperature is correlated with lower happiness	Warm winter, cold summer, low rain, windy	Convex hulls are separeted but second component only has temp variables as significant

DiCA Inference

Grouping variables to observe relative effect among variables

PLS-C

Methods	Unhappy	Normal	Very Happy	Reliability
PCA	Others	Temp & Rain	N/A	Components have significant contribution but convex hull has overlapping areas and Component 2 & 7 contradicts
MCA	warm summers, cold winters, high rain	N/A	Warm winter, cold summer, low rain	Components have significant contribution but convex hull has overlapping areas
DiCA	warm summers, cold winters, high rain	Higher variation in temperature is correlated with lower happiness	Warm winter, cold summer, low rain, windy	Convex hulls are separeted but second component only has temp variables as significant
PLS-C	Rain	Temp	Temp	Second component has more rain variables as significant than temp variables

Multi Factor Analysis

Methods	Unhappy	Normal	Very Happy	Reliability
PCA	Others	Temp & Rain	N/A	Components have significant contribution but convex hull has overlapping areas and Component 2 & 7 contradicts
MCA	warm summers, cold winters, high rain	N/A	Warm winter, cold summer, low rain	Components have significant contribution but convex hull has overlapping areas
DiCA	warm summers, cold winters, high rain	Higher variation in temperature is correlated with lower happiness	Warm winter, cold summer, low rain, windy	Convex hulls are separeted but second component only has temp variables as significant
PLS-C	Rain	Temp	Temp	Second component has more rain variables as significant than temp variables
MFA	Partial factors dominated by Temp, then rain and other variables	Neither of partial factors seems to have sufficient effect	Partial factors dominated by Temp and other variables, lesser effect of rain	Convex hull has overlapping areas

Cluster Analysis - DiSTATIS

Kmeans

Conclusion

• MCA and DiCA agrees:
  • Warmer winter, colder summer, low rain, windy cities makes people happy
  • Colder Winter, warmer summers, high rain, less windy makes people unhappy

However, even though MCA shows that most the variables has high contribution for the strongest signal in the data - DiCA shows that temp, rain and wind variables contributes significantly.

Hence,

• Happiness doesn’t seem to be highly correlated to environmental conditions
• Temperature, rain and wind seem to be slightly correlated with happiness.
• Cluster Analysis doesn’t seem to show any patterns in the data.