This is from an Applied Mixed Models class. Please answer problem #4 (b). Attached are the information you will need to answer this problem. Background: The novel Coronavirus designated SARS-CoV-2 appeared in December 2019 to initiate a pandemic of respiratory illness known as COVID-19, which had been an unprecedented global public health crisis, and the safe and effective COVID-19 vaccinations are vital for the global strategy to combat the pandemic. However, the population must reach a sufficient vaccination rate, i.e. 6070%, to achieve herd immunity. Vaccine hesitancy, or "delay in acceptance or refusal of vaccination despite availability of vaccination services", could affect vaccination rate and the ability to establish herd immunity. Factors that affect the attitude towards acceptance of vaccination include: complacency (do not perceive a need for a vaccine), convenience (access) and confidence (do not trust vaccine or provider). Therefore, determining the factors associated with COVID-19 vaccine hesitancy are important for public health developing strategies targeting the voluntarily vaccine-hesitant individuals. To evaluate the vaccination compliance rates of individuals living in the U.S., a longitudinal study was used to examine the individual's attitudes toward vaccines over a six-month period. Beginning in March 2020 (early phase of the pandemic), researchers collects attitudes from a cohort of the same participants, N=407, every month. The primary outcome was the COVID-19 Vaccine Hesitancy Score (vhs19), which can range between 0 and 100, with higher scores indicating lower COVID-19 vaccine hesitancy, i.e. more positive attitude toward vaccination. Additional available data included ID=month=gender=age=SES= political=ParticipantIDnumber.Timeofdatacollectionasfollowsmonth=1(March2020),2(April2020),,6( August2020).Genderindicator,e.g.0=female,1=male.Ageofparticipantatthebaseline,i.e.month=1. Socioeconomicstatus,e.g.0=lowSES,1=highSES.Participantspoliticalpartyaffiliation,e.g.0= Democratic,1=Republican. The primary goal of the analysis is to investigate whether or not evidence for vaccine attitudes (vhs19) exists with respect to political party affiliation (political) during an unprecedented public health crisis. Figure 1 in the Appendix A reports a plot with vaccination attitudes by political party affiliation for each participant profiles (March-August 2020). Note that we may only focus on a few of the available covariates in the dataset for this problem.4. (10 points) The remainder of the question concerns some plausible extensions of modeling effort. You can choose an appropriate model to answer this question. (a) (5 points) It is hypothesized that the rate of change in vhs 19 is the same by political group for the first two months, then differs by group after that. Write down an appropriate model to address this scientific hypothesis (denote your model parameters by 0,1,,P ). (b) (5 points) You may ignore part (a) from here on..

1. This is from an Applied Mixed Models class. Please answer problem #4 (b). Attached are the
information you will need to answer this problem.
Background: The novel Coronavirus designated SARS-CoV-2 appeared in December 2019 to
initiate a pandemic of respiratory illness known as COVID-19, which had been an unprecedented
global public health crisis, and the safe and effective COVID-19 vaccinations are vital for the
global strategy to combat the pandemic. However, the population must reach a sufficient
vaccination rate, i.e. 6070%, to achieve herd immunity. Vaccine hesitancy, or "delay in acceptance
or refusal of vaccination despite availability of vaccination services", could affect vaccination rate
and the ability to establish herd immunity. Factors that affect the attitude towards acceptance of
vaccination include: complacency (do not perceive a need for a vaccine), convenience (access)
and confidence (do not trust vaccine or provider). Therefore, determining the factors associated
with COVID-19 vaccine hesitancy are important for public health developing strategies targeting
the voluntarily vaccine-hesitant individuals. To evaluate the vaccination compliance rates of
individuals living in the U.S., a longitudinal study was used to examine the individual's attitudes
toward vaccines over a six-month period. Beginning in March 2020 (early phase of the pandemic),
researchers collects attitudes from a cohort of the same participants, N=407, every month. The
primary outcome was the COVID-19 Vaccine Hesitancy Score (vhs19), which can range between
0 and 100, with higher scores indicating lower COVID-19 vaccine hesitancy, i.e. more positive
attitude toward vaccination. Additional available data included ID=month=gender=age=SES=
political=ParticipantIDnumber.Timeofdatacollectionasfollowsmonth=1(March2020),2(April2020),,6(
August2020).Genderindicator,e.g.0=female,1=male.Ageofparticipantatthebaseline,i.e.month=1.
Socioeconomicstatus,e.g.0=lowSES,1=highSES.Participantspoliticalpartyaffiliation,e.g.0=
Democratic,1=Republican. The primary goal of the analysis is to investigate whether or not
evidence for vaccine attitudes (vhs19) exists with respect to political party affiliation (political)
during an unprecedented public health crisis. Figure 1 in the Appendix A reports a plot with
vaccination attitudes by political party affiliation for each participant profiles (March-August 2020).
Note that we may only focus on a few of the available covariates in the dataset for this problem.4.
(10 points) The remainder of the question concerns some plausible extensions of modeling effort.
You can choose an appropriate model to answer this question. (a) (5 points) It is hypothesized that
the rate of change in vhs 19 is the same by political group for the first two months, then differs by
group after that. Write down an appropriate model to address this scientific hypothesis (denote
your model parameters by 0,1,,P ). (b) (5 points) You may ignore part (a) from here on. Now
reviewers of the research ask the research to determine if there is heterogeneity in the rate of
change of vhs19 among participants (conditional upon political affiliation). Can your chosen model
address reviewers' question? If yes, state explicitly how you would go about testing whether or not
there was heterogeneity in the rate of change of vhs19 among participants. If not, explain your
reasoning.Appendix B #### Model modA > osfcovid19.Aug = subset(osfcovid19, month == 6) >
modA =lm( vhs 19 political + age, data = osfcovid19.Aug) > summary (modA) lm( formula = vhs19
political + age, data = osfcovid19.Aug) Coefficients: Residual standard error: 2.098 on 404
degrees of freedom Multiple R-squared: 0.8691 , Adjusted R-squared: 0.8685 F-statistic: 1342 on
2 and 404 DF, p-value: <2.2e16 >confint(modA) (Intercept)politicalage2.5%65.613494478
11.2000306140.00157455397.5%67.0683940210.380946120.03955191 #### Confounder:

2. gender >modA1=lm( vhs 19 gender, data = osfcovid19.Aug) >summary(modA1) Coefficients:
(Intercept)genderEstimate62.17041.0731Std.Error0.40190.5719tvalue154.6961.876Pr(>t)<2e16
0.0613. >modA2=lm (political gender, data = osfcovid19.Aug) >summary(modA2)
Coefficients:Appendix C #### Model modB #### Model modC > modC = gls(vhs19 age +
month*political + month*SES + month*gender, + data = osf covid19, + correlation =
corCompSymm (form =1 ID), method = 'ML') > summary (modC) Generalized least squares fit by
maximum likelihood Model: vhs19 age + month political + month SES + month gender Data:
osfcovid19 AIC BIC logLik 10551.7110615.515264.854