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  1. Random Component: Distribution of { Y t | Y t - 1 , } belongs to the exponential family of distributions.
    f ( y t ; θ t , φ | F ) = e x p y t θ t - b ( θ t ) a t ( θ t ) + c ( y t , φ ) ,
    where θ t is the parameter of the distribution and φ is a dispersion parameter. In the Poisson case, we have: a t ( φ ) = 1 ; θ t = log ( μ t ) ; b ( θ t ) = μ t ; c ( y t ; φ ) = - log y .
  2. Systematic Component: μ t , the mean of Y t , is modeled by a monotone link function g ( · ) such that
    g ( μ t ) = X t T β ,
    where X is the set of covariates and β is a vector of coefficients. In the Poisson case μ = λ , g ( λ ) = log ( λ ) .

In the case of time series data, we can augment the exogenous covariates in the model with lagged values of the response variable, i.e. the observed counts at previous time points. Thus the model is “observation-driven.” Lags of exogenous covariates can also be included. For instance let the new covariate matrix be represented by Z , where

Z t T = ( X t , X t - 1 , , X t - p , Y t - 1 , , Y t - n ) .

For more details see [link] .

Clustering of tsc models

Armed with the GLM model for Poisson regression, we can begin clustering the TSC. In order to determine the similarity or dissimilarity between two TSC, a metric is needed to measure the “distance.” The classic Euclidean metric is not adequate for data with time dependence. We will use the empirical Kullback-Leibler (KL) likelihood metric [link] , which calculates the distance between two TSC by evaluating the relative fit of their respective models.

Let λ j be a given “model structure” for the data, i.e. an observation-driven Poisson model with specified covariates. The KL metric has the following expression.

D K ( λ k , λ j ) = 1 | Y K | y Y K ( log p ( y | λ k ) - log p ( y | λ j ) )

where Y K is the set of data objects which belong to cluster k . Note that log p ( y | λ k ) is an expression for the likelihood of the model. See [link] for discussion on the likelihood of observation-driven Poisson models. The measure is made symmetric by,

D S K = D K ( λ k , λ j ) + D K ( λ j , λ k ) 2

With the KL metric, we apply a hierarchical bottom-up clustering algorithm. A flowchart of the algorithm is displayed in Figure 1.

The MBC algorithm

The algorithm produces a cluster tree similar to the figure below. The bottom-up clustering method is easy to visualize and break down objects into groups and eliminates the need for any stopping criterion.

Sample hierarchical cluster tree


Finding relevant data

Though count data are prevalent in consumer behavior, obtaining commercial commercial data for MBC is expensive. Thus, for this project, we use results from previous studies on marketing data to creat a data set that realistically mimics consumer behavior.

Data simulation

Niraj et al. [link] proposed an economic model for consumer purchases of bacon and eggs. Based on store scanner data, the authors studied the consumer sensitivities to various variables such as personal utility, product prices, product displays, and purchase history. For the purpose of data simulation, key elements from this economic model were borrowed to create our own consumer bacon and eggs purchase data.

We let Y b , t and Y e , t be a bivariate Poisson random variable which represent a consumer's purchase of bacon and eggs during time window t respectively, then Y b , t and Y e , t can be modeled using a trivariate reduction [link] :

Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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