THis is from an Applied Mixed Models class. Answer just part (a). 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.3. (20 points) Now refer to the model modC in Appendix C. (a) (5 points) Suppose we consider male and low socioeconomic status group, write down expressions for the rate of change of vhs 19 in May 2020 , i.e. month =3, for each political affiliation. (b) (5 points) From part (a) and the output of model modC, compute an estimate of difference in the mean vhs 19 between two political affiliations in May 2020. (c) (5 points) Suppose that researchers fitted model modC by using restricted maximum likelihood (REML) method, will your answer in part (b) change? .

1. THis is from an Applied Mixed Models class. Answer just part (a).
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.3.
(20 points) Now refer to the model modC in Appendix C. (a) (5 points) Suppose we consider male
and low socioeconomic status group, write down expressions for the rate of change of vhs 19 in
May 2020 , i.e. month =3, for each political affiliation. (b) (5 points) From part (a) and the output of
model modC, compute an estimate of difference in the mean vhs 19 between two political
affiliations in May 2020. (c) (5 points) Suppose that researchers fitted model modC by using
restricted maximum likelihood (REML) method, will your answer in part (b) change? Briefly explain
your reasoning. Page 3 (d) (5 points) Which model, modB or modC, would you choose? Justify
your answer.Appendix C #### Model modB #### Model modC