Estimating Planned Sales Call Frequencies with Incomplete Information Using the EM Algorithm

• Activity Number: 186
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Statistics in Business Schools Interest Group
• Author(s): Lan Nygren* and Lewis Coopersmith
• Companies: Rider University and Rider University
• Keywords: EM algorithm ; Incomplete information ; Multinomial cell probabilities ; Sales call frequencies ; Diary survey

Abstract

We consider estimating planned sales call frequencies of a selling company with incomplete information caused by short recording durations in diary surveys. For practical reasons, it is necessary to keep the recording period short. Missing data occur when the recording period is not long enough to include observations with low call frequencies. We derive the maximum likelihood estimators of the multinomial cell probabilities for the planned sales call frequencies using the expectation maximization (EM) algorithm. We show that the EM algorithm estimators have good asymptotic properties in terms of both bias and mean squared error (MSE) and are more accurate and reliable than the estimators obtained by the na\"{i}ve approach of treating the absence of a sales call as a non-called on respondent (i.e., zero frequency). The effect on the estimators when the number of frequency classes increases is also investigated.