Applied Multivariate Analysis I EDUC 771 Problem Set 3 1. Using the matrix X below
!1 2 1 4 1 $ # 2 1 2 2 5& # & X = #1 0 1 0 3 & # & # 3 1 0 5 2& # 2 1 3 1 7& " %
Determine if the rows/columns are linearly independent. How do you know? What is the
Other Unconstrained Ordination Techniques
Linear
P Factor analysis (FA)
P Multidimensional scaling (MDS/PCO)
P ML-Unconstrained linear ordination (ULO)
Quadratic
P Correspondence analysis (CA & DCA)
P ML-Unconstrained quadratic ordination (UQO)
Smooth
P M
Cluster Analysis
1
2
3
Can we organize
sampling entities into
discrete classes, such that
within-group similarity is
maximized and amonggroup similarity is
minimized according to
some objective criterion?
4
Sites
1
2
3
4
5
6
5
A
1
1
1
10
10
10
Species
B
9
Step 5: Conduct Analysis
Model Parameterization:
P Dropped species with fewer than 5 occurrences
P Log-transformed species abundances
P Row-normalized species log abundances (chord distance)
P Selected smallest best
subset of variables from each
set of in
Variance Decomposition of
Species-Environment Relationships
P Goal is to decompose the variance in the species data
set explainable by logical components of unique and
interactive effects of explanatory variables.
Total
Inertia
S
% species
variance
explai
Data Screening and Adjustments
Purpose:
P Detect and correct data errors
P Detect and treat missing data
P Detect and handle
insufficiently sampled
variables (e.g., rare species)
P Conduct transformations and
standardizations
P Detect and handle outliers
Multivariate Statistics
Summary and Comparison of Techniques
P The key to multivariate statistics is understanding
conceptually the relationship among techniques with
regards to:
< The kinds of problems each technique is suited for
< The objective(s) of e
Polythetic Divisive Hierarchical Clustering
P PDHC techniques use the information on
all the variables.
P PDHC begins with all entities together in a
single cluster and successively divide the
entities into a hierarchy of smaller and
smaller clusters unti
EDUC 771: Applied Multivariate Analysis What is multivariate analysis and how is it different from univariate analysis? There are two ways that multivariate analysis is conceptualized: an analysis that considers several variables being measured for e
Applied Multivariate Analysis I Final Problem Set Directions: This exam is open book and open notes, open internet, open library, etc. It is not open for discussion with anyone else except me. Please present your answers neatly and clearly. The point
EDUC771: Applied Multivariate Analysis Problem Set 2
1. The matrices A, B and C are given below:
3 5 0 A = 1 2 1 3 7 1
3 1 -1 B = 5 2 0 1 1 -1
(i) (ii) (iii) (iv)
Add the two matrices together using SPSS. Compute the product using
November 19, 2003 Before we begin, I want to address the question of comparing means. If we have 4 means that we want to compare, we have: H 0 : 1 = 2 = 3 = 4 If we want to test this hypothesis, we reconceptualize it as: H 0 : 1 - 2 = 0
2 - 3 =
Discrimination Among Groups
Id
1
2
3
.
31
32
60
.
61
62
90
Species Canopy Snag
Canopy
Cover
Density Height
A
A
A
.
B
B
B
.
C
C
C
80
75
72
.
35
75
15
.
5
8
25
1.2
0.5
2.8
.
3.3
4.1
5.0
.
2.1
3.4
0.6
35
32
28
.
15
25
3
.
5
2
15
1
Discrimination Among Groups