FUNCTIONAL PRINCIPAL COMPONENT ANALYSIS WITH APPLICATION TO VIEWERSHIP OF MOTION PICTURES

Abstract

Principal Component Analysis (PCA) is one widely used data processing technique in application, especially for dimensionality reduction. Functional Principal Component Analysis (fPCA) is a generalization of ordinary PCA, which focuses on a sample of functional observations and projects the original functional curves to a new space of orthogonal dimensions to capture the primary features of original functional curves. While, fPCA suffers from two potential error sources. One error source is originated from truncation when we approximate the functional subject's expansion; The other stems from estimation when we estimate the principal components from the sample. We first introduce a generalized functional linear regression model and propose it in the Quasi-likelihood setting. Asymptotic inference of the proposed functional regression model is developed.

We also utilize the proposed model to help marketing operational decision process by analyzing viewership of motion pictures. We start with discussing customer reviews effect on movie box office sales. We use the functional regression model with function interactions to measure the effect of Word-of-Mouth on movie box office sales. One main challenge of modeling with functional interactions is the interpretation of model estimate results. We demonstrate one method to help us get important insights from model results by plotting and controlling a re-labbeld 3-D plot.

Apart from movie performance in theater, we also employ functional regression model to predict movie pre-release demand in Video-on-Demand (VOD) channel. As its growing popularity, VOD market attracts much attention in marketing research. We analyze the prediction accuracy of our proposed functional regression model with spatial components and find that our proposed model gives us the best predictive accuracy.

In summary, the dissertation develops asymptotic properties of a generalized functional linear regression model, and applies the proposed model in analyzing viewership of motion picture both in theater and Video-on-Demand channels. The proposed model not only advances our understanding of motion picture demand, but also helps optimize business decision making process.