This is from Applied Mixed Model Class. Please answer problem # 4 (a). Attached are all the information you 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.