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SOST20131/30031 Statistical Models
创建日期：2024-04-24 18:11:09
所属分类：统计学statistics
标签： SOST20131
Statistical Models

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SOST20131/30031 Answering Social Research Questions with Statistical Models

2021
Assessment part 2 (60% of course grade):
Lack of physical activity and depression
Major clinical depression can be a severely debilitating illness, but even mild depressive episodes can
severely affect quality of life. Roshanaei-Moghaddam et al. (2009) reviewed the relationship
between physical activity and depression. There is certainly a negative correlation between physical
activity and depression, such that lower levels of activity are associated with higher levels of
depression and vice versa, but it is unclear as to the size of the causal relationship. For example,
there may be confounding factors, such as attributes of individuals that make them both more likely
to engage in physical activity and less likely to suffer depression.
In an effort to disentangle spurious from causal effects, you have decided to analyse data from the
English Longitudinal study of Ageing (ELSA). This study surveyed a sample of English householders
aged 50 or more, across multiple occasions, two years apart. The first occasion, or wave, was in 2002
and the second wave was in 2004.

Data
The variables shown in Figure 1 were measured in ELSA. These variables are described in Table 1,
below. These data are contained in the file “elsa12wide.csv”. The key relationships you wish to
analyse are shown by the arrows drawn with dashed lines in Figure 1.

male1
age1
cesd1
notact1
illness1
cesd2
notact2
Figure 1: Directed Acyclic Graph of the hypothesised causal relationships
between lack of physical activity (notact1 & notact2) and depression
(cesd1 & cesd2) across two waves of ELSA.
2

Table 1: Variables from the DAG in Figure 1, as measured in the English Longitudinal Study of
Ageing (ELSA), in the file “elsa12wide.csv”.
Variable Description Coding
0. id Unique identifying label for each respondent arbitrary numerical label
1. age1 Chronological age in wave 1 (2002) Years since birth
2. male1 Biological sex in wave 1 Male = 1, female = 0
3. illness1 Limiting longstanding illness, self-declared in
wave 1
Has illness = 1, no illness = 0
4. cesd1 Centre for Epidemiological Studies’ Depression
(cesd) scale score, wave 1
Score from 0 to 8 (higher score =
more depressed)
5. cesd2 as above, in wave 2 (2004) as above
6. notact1 Self-declared lack of moderate physical activity
at least once a week, in wave 1
1 = no moderate physical activity
at least once a week,
0 = at least some moderate
physical activity
7. notact2 as above, in wave 2 as above

Questions to answer
Use the R package and the data contained in “elsa12wide.csv” to carry out these tasks and answer
these questions.
1. Fit a model for the unconditional effect of notact1 -> cesd2 (i.e. a model with cesd2 as the
outcome and notact1 as the sole predictor, and no additional “third” variables).
a. Discuss the statistical and substantive meaning of the estimated model results (e.g.
b parameters & SEs, p-values, R-square, whether it is likely a causal effect). [6 marks]
b. Discuss the assumptions of this model (causal and statistical), and how they affect
what you can conclude about the relationship between physical activity and
depression in the study population. [6 marks]
2. Based upon the DAG in Figure 1, specify and fit a model to evaluate the total causal effect of
notact1 -> cesd2.
a. Explain the reasoning behind your choice of model specification, i.e. which variables
did you choose to include as additional predictors in the model, if any. [10 marks]
b. Discuss the changes in the estimated model results (e.g. b parameters, SEs, p-values,
R-square), and their statistical and substantive meanings. [10 marks]
c. Discuss the assumptions of this model (causal and statistical), how they differ from
those you discussed in 1.b. above, and how they affect what you can conclude about
the relationship between physical activity and depression in the study population. [8
marks]
3. Fit a model for the unconditional effect of cesd1 -> notact2 (i.e. a model with notact2 as the
outcome and cesd1 as the sole predictor, and no additional “third” variables).
a. Discuss the statistical and substantive meaning of the estimated model results (e.g.
b parameters, SEs, p-values, R-square). [10 marks]
b. Discuss the assumptions of this model (causal and statistical), and how they affect
what you can conclude about the relationship between depression and physical
activity in the study population. [5 marks]
3

4. Based upon the DAG in Figure 1, specify and fit a model to evaluate the total causal effect of
cesd1 -> notact2.
a. Explain the reasoning behind your choice of model specification, i.e. which variables
did you choose to include as additional predictors in the model, if any. [10 marks]
b. Discuss the changes in the estimated model results (e.g. b parameters, SEs, p-
values), and their statistical and substantive meaning. [10 marks]
c. Discuss the assumptions of this model (causal and statistical), how they differ from
those you discussed in 3.b. above, and how they affect what you can conclude about
the relationship between physical activity and depression in the study population.
[10 marks]
5. Consider together the models from questions 2. and 4. Did you use the same predictor
variables in each model or different ones, and why? How did they vary in terms of model fit?
When viewed together, what do the results from these models tell us about the relationship
between physical activity and depression in the study population? [15 marks]
Copy/past the R script that you used to run the models for the questions above into an appendix of
your submission. [You will not be graded on the correctness of this appendix. Marks will neither be
awarded nor penalized for your R code. Rather it will be used to help in the understanding your
models and results. Failure to include an R appendix will result in a penalty of 10 marks.]
Guidance notes
 Your submission should answer each of the 5 questions above.
 You should use the models we discussed in class to answer the questions, i.e. a linear model
(a.k.a. linear regression, multiple linear regression, general linear model) or a binary logistic
model (a.k.a. logistic regression, generalized linear model). Different questions may require
different models, so be sure to mention briefly which model you chose and why.
 Good answers are those that clearly address all parts of the question.
 Use descriptive statistics and/or derived quantities (such as model-predicted values) to
support and justify your answers, where this will help you to answer the question clearly.
 You may re-code, centre, and / or derive new variables if it will help you answer the
questions. Be sure to clearly describe and justify any such manipulation of the data.
 Your answers to questions 2.b. and 4.b. will be marked without regard to whether you
answered questions 2.a. and 4.a. correctly, i.e. even if you got questions 2.a. or 4.a. wrong, it
is still possible to get full marks for questions 2.b., 4.b.
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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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