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  • 1. MULTIVARIATE DATA ANALYSIS- AGLIMPSE FDP conducted @ NITC CalicutBy Arun Kumar. S

2. Quote of the dayStatistics is the science that addresses thetwin question: what data should becollected, and, once collected, how shouldthey be analyzed?- W.G. HUNTER 3. Can Statistics be trusted?There are three kinds of lies: Lies, damnedlies, and statistics. -- Mark Twain 4. Doing research(PhD) No end Time constraints Age constraints Your own capability Importance of friends/family . . . Improving writing and analytical(researchmethodology) skills.. 5. Steps in Research process Course work Mini project Literature survey Choosing research problem-Accomplishableresearch Research plan Prepare questionnaire Collect data Analyze data Publish or perish Thesis writing 6. Which test should I use ? 7. Indicators 8. Multivariate analysis An extension to univariate (with a singlevariable) and bivariate (with two variables)analysis Dealing with a number of samples andspecies/environmental variablessimultaneously 9. Multivariate analysis techniques Multiple Regression Analysis Logistic Regression Analysis Discriminant Analysis Multivariate Analysis of Variance (MANOVA) Factor Analysis Cluster Analysis Multi-dimensional Scaling Correspondence Analysis Conjoint Analysis Canonical Correlation Structural Equation Modelling 10. Multivariate Data Set Morphological measurement of organisms (e.g. length) Physiological measurement of organisms (e.g. bloodpressure) Physiochemical measurement of the environment (e.g.air temperature) Species abundance Species richness etc 11. Why MVA? Situation 1: A harried executive calls you into his office andshows you three proposed advertising campaigns for nextyear. He asks, Which one should I use? They all look prettygood to me. Situation 2: During the annual budget meeting, the salesmanager wants to know why two of his main competitors aregaining share. Do they have better widgets? Do their productsappeal to different types of customers? What is going on inthe market? 12. Multidimensional Scaling A mathematical dimension reduction technique that maps thedistances between observations in a high dimensional spaceinto a lower (for example, two) dimensional space. There are two types of MDS: -Metric-Non-metric 13. Data Type. Metric MDS: Assume the input data is either interval or ratioduring measurement (Quantitative ) Non-metric MDS (nMDS) The data should be in the form of rank(Quantitative and/or Qualitative) 14. Major Advantages of nMDS Ordination is based on the rankedsimilarities/dissimilarities between pairs ofsamples. The actual values of data are notbeing used in the ordination, fewassumptions on the nature and quality ofthe data Ordinal data could be usede.g. 1 = very low; 2 = low; 3 = mid; 4 = high; 5 = very high 15. How does MDS Work?MDS attempts to locate the n observations in areduced dimensional space so that the differencesbetween pairs of points in this reduced spacematch, as closely as possible, the true-ordereddifferences between the observations 16. Data Envelopment Analysis (DEA) DEA, initiated by Charnes, Cooper and Rhodes (CCR)(1978) and building on Farells (1957) work wasfurther generalized by Banker, Charnes and Cooper(BCC) (1984). non-parametric linear programming technique relative efficiency of decision-making units (DMUs) The method utilizes linear programming to envelopobserved data and then calculate efficiency based onthe distance a unit is firm the relatively efficientfrontier (the envelope). Widely used in recent literature 17. A DEA model can be constructed either tominimise inputs or to maximise outputs. Aninput orientation aims at reducing the inputamounts as much as possible while keeping atleast the present output levels, while anoutput orientation aims at maximising outputlevels without increasing use of inputs(Cooper et al., 2000). 18. Steps in DEA Identify the objective function Identify the Inputs and outputs Collect the data Make the assumptions of the model Input oriented or output oriented Select the software to run DEA Report the results 19. Objectives of DEA To measure the technical efficiency ofdifferent departments in XYZ university in theyear 2005-06 To measure the allocative efficiency of asample of manufacturing firms in India duringthe period 2009-2010 To measure the scale efficiency of sample ofnationalized banks in Trichy city in 2010-2011 20. Can find out . . . single efficiency score it highlights the areas of improvement foreach single DMU able to identify whether it has used inputexcessively or its output has been under-produced. The set of efficiency DMUs is called thereference set. 21. Conditions for implementing DEA DMUs to be sufficiently similar, so that comparisons are meaningful. similar range of resources is available to all theunits and they operate in a similarenvironment. 22. It is to be noted that those DMUs indicated as efficientare only efficient in relation to others in the sample. Efficiency scores from DEA analyses are known to behighly sensitive to both the choice of input and outputmeasures and the inclusion or exclusion of keyvariables. A serious drawback of DEA is that it does notprovide tests of significance of the input or outputvariables included inthe model. 23. DEA software Efficiency Measurement Systems(EMS) Data Envelopment Analysis Program(DEAP)Tim Coelli 1996 MS Excel Spreadsheet for DEA computations 24. Rule of thumb DMUs must be homogenous units or the oneswith similar objectives. The no: of DMUs is expected to be larger than theproduct of no: of inputs and outputs in order todiscriminate effectively between efficient andinefficient DMUs The sample size should be at least 2 or 3 timeslarger than the sum of the no: of inputs andoutputs