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Multivariate methods

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Multivariate methods

Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis.

Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical implementation of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the actual problem being studied.

In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both

  • how these can be used to represent the distributions of observed data;
  • how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis.

Certain types of problem involving multivariate data, for example simple linear regression and multiple regression, are not usually considered as special cases of multivariate statistics because the analysis is dealt with by considering the (univariate) conditional distribution of a single outcome variable given the other variables.

Multivariate work that we have done in the past include:

  • Marketing Response – prediction techniques used to enhance the likelihood of customers responding to marketing campaigns for one of the most recognised and respected organisations in New Zealand. Previously the company had selected targets at random from their customer database and endured response rates around 0.5%. The prediction model that was derived resulted in response rates around 3.5%, a seven fold increase on the previous approach. This piece of work also included the development of a surrogate model to enable the organization to interpret the complex model that was best performed.
  • Prediction Model – constructed for a major Australian retailer, this predicted the likelihood of a customer to be contestable, i.e. to shop with a major competitor. Rich internal data was available for a percentage of customers and this data set was manipulated to reflect market share before a model was built. The results were applied to the remainder of the customer data base, which allowed the retailer to undertake targeted marketing campaigns at those customers with a higher propensity to be contestable.
  • Patron Prediction – US casino property data utilised to construct a pilot model for predicting the long term likelihood of a patron being valuable based off their first visit metrics.
  • Occupancy – Model developed for major Sydney hotel, which looked at likelihood of hotel occupancy reaching a certain threshold a fixed period of time out from the date in question. This could be used to make strategic decisions around raising/lowering tariffs based on what the likely occupancy of was.
  • Australasian Horse Racing Prediction Model(s) – investigated and constructed prediction models for the purposes of wagering. 20 years of race results for all meetings conducted in Australia and NZ were sourced in order to build prediction models. In excess of 4 million records were available, which required cleansing, matching and validation. Variables were derived from the raw indput data. Data driven markets were produced on a daily basis for every NZ horse race.
  • Match Prediction – a number of individual sports models were developed over the years that predict match outcome, margin and likelihood of victory. Coupled with an appropriate set of rules related to staking. These models are used to identify and exploit inefficiencies in wagering markets.