Statistical techniques for studying the impact of climate change on crop production - Climate Change Effect on Crop Productivity - page 140

basis of population densities and the frequency and persistence
of outbreaks. The analysis can be used to improve regional
monitoring and control of pest populations. Clustering tech-
niques require that one define a measure of closeness or simi-
larity between two observations. Clustering algorithms may be
hierarchical or non-hierarchical. Hierarchical methods can be
either agglomerative or divisive. An agglomerative hierarchical
method starts with the individual objects, thus there are as many
clusters as objects. The most similar objects are first grouped
and these initial groups are merged according to their similari-
ties. Eventually, as the similarity decreases, all sub-groups are
fused into a single cluster.
Divisive hierarchical methods work in the opposite direction.
An initial single group of objects is divided into two sub-groups
such that the objects in one sub-group are far from the objects in
the others. These sub-groups are then further divided into dis-
similar sub-groups. The process continues until there are as many
sub-groups as objects, that is, until each object forms a group. The
results of both an agglomerative and divisive method may be dis-
played in the form of a two-dimensional diagram known as den-
drogram, which illustrates the mergers or divisions that have been
made at successive levels. K-means clustering is a popular non-
hierarchical clustering technique. It begins with user-specified
clusters and then reassigns data on the basis of the distance from
the centroid of each cluster. See Johnson and Wichern (2006) and
Hair et al. (2006) for more detailed explanations.
Discriminant analysis is a multi-variate technique concerned
with classifying distinct set of objects (or set of observations)
and with allocating new objects or observations to the previ-
ously defined groups. It involves deriving variates, which are a
combination of two or more independent variables that will dis-
criminate best between a priori defined groups. The objectives
of discriminant analysis are (i) identifying a set of variables
that best discriminates between the groups, (ii) identifying a
new axis, Z, such that new variables Z, given by the projec-
tion of observations onto this new axis, provides the maximum
separation or discrimination between the groups and (iii) clas-
sifying future observations into one of the groups.
References
Box, G.E.P. and Jenkins, G.M. 1970. Time Series Analysis:
Forecasting and Control . Holden-Day, San Francisco.
Cox, D.R. 1958. The regression analysis of binary sequences (with dis-
cussion). Journal of the Royal Statistical Society B, 20 , 215-242.