代写SMM540、代写R语言编程

日期：2022-11-03 09:00

SMM540 Group Coursework 1 2022

Deadline 4 November 2022

1. Consider the dataset ObesityData.csv available on Moodle. For a description of the variables refer

to the pdf file ObesityData_description.

Perform a principal component analysis and report your conclusions. (Not more than 250 words,

excluding R codes, plots, tables etc.).

[Total marks: 15]

2. On the same dataset (ObesityData.csv) perform a multidimensional scaling, comment on your re-

sults and compare with those obtained using the PCA above. (Not more than 250 words, excluding

R codes, plots, tables etc.)

[Total marks: 10]

3. A factor analysis was carried out of a data matrix of variables relating to the occupational and

educational status of three generations of family members. A description of the ten variables used

in the analysis is given in Table 1.

Variable Generation Code Description

x1 1 HF/O Husband’s father’s occupational status

x2 1 WF/O Wife’s father’s occupational status

x3 2 H/FE Husband’s further education

x4 2 H/Q Husband’s qualifications

x5 2 H/O Husband’s occupational status

x6 2 W/FE Wife’s further education

x7 2 W/Q Wife’s qualifications

x8 3 FB/FE Firstborn’s further education

x9 3 FB/Q Firstborn’s qualifications

x10 3 FB/O Firstborn’s occupational status

Table 1: Descriptions of social mobility variables.

(a) The unrotated factor loadings obtained from the three-factor model are given in Table 2.

Interpret them. [Marks: 7.5]

α?i1 α?i2 α?i3

x1 HF/O 0.426 0.403 0.053

x2 WF/O 0.404 0.343 0.008

x3 H/FE 0.592 -0.026 0.116

x4 H/Q 0.558 -0.240 0.118

x5 H/O 0.575 0.481 0.031

x6 W/FE 0.451 -0.126 0.369

x7 W/Q 0.477 -0.296 0.462

x8 FB/FE 0.615 -0.191 -0.289

x9 FB/Q 0.519 -0.358 -0.381

x10 FB/O 0.602 0.168 -0.219

Table 2: Loading matrix giving the unrotated loadings from a three-factor model of the social mobility

data.

(b) Rotations can be carried out to determine whether simple structure can be achieved. The

factor loadings obtained from an orthogonal (varimax) rotation and an oblique (oblimin)

rotation of the three-factor solution are shown in Tables 3 and 4. Comment on the results.

[Marks: 7.5]

(Not more than 250 words.)

[Total marks: 15]

α?i1 α?i2 α?i3

x1 HF/O 0.576 0.042 0.111

x2 WF/O 0.516 0.086 0.090

x3 H/FE 0.329 0.288 0.416

x4 H/Q 0.135 0.360 0.485

x5 H/O 0.728 0.113 0.144

x6 W/FE 0.163 0.078 0.568

x7 W/Q 0.042 0.106 0.718

x8 FB/FE 0.209 0.645 0.194

x9 FB/Q 0.018 0.723 0.140

x10 FB/O 0.491 0.434 0.098

Table 3: Loading matrices giving the varimax rotated loadings from a three-factor model of the social

mobility data

α?i1 α?i2 α?i3

x1 HF/O 0-0.064 0.599 0.025

x2 WF/O -0.003 0.530 0.002

x3 H/FE 0.183 0.246 0.353

x4 H/Q 0.279 0.015 0.445

x5 H/O -0.016 0.747 0.025

x6 W/FE -0.051 0.074 0.585

x7 W/Q -0.032 -0.085 0.765

x8 FB/FE 0.637 0.101 0.058

x9 FB/Q 0.762 -0.109 0.014

x10 FB/O 0.381 0.452 -0.052

Table 4: Loading matrices giving the oblimin rotated loadings from a three-factor model of the social

mobility data.

4. Read the paper ”Modeling longevity risks using a principal component approach: A comparison

with existing stochastic mortality models” by Sharon S. Yanga, Jack C. Yueb and Hong-Chih

Huangc (2010) available on Moodle. Write a report (not more than 3 pages) summarising the

goals of the work [2], the data source [2], the methods used [4], the results of the analysis and the

conclusions [6]. Also, comment on the robustness and generality of the results, the limitations of

the analysis and possible improvements [6].

[Total marks: 20]