Fix grammatical errors in vignettes

Author: trannttoan

README.md

@@ -32,7 +32,7 @@ shinymrp::run_app()
 
 Explore the Shiny app without installation via our [online demo](https://mrpinterface.shinyapps.io/shinymrp/).
 
-Need a walkthrough? Watch our step-by-step [video tutorial](https://youtu.be/CUcRYn92fmU?si=EhcAbuwuG2XM-0N0).
+Need a walk-through? Watch our step-by-step [video tutorial](https://youtu.be/CUcRYn92fmU?si=EhcAbuwuG2XM-0N0).
 
 ### Object-Oriented Programming Interface
 

vignettes/data-prep.Rmd

@@ -182,7 +182,7 @@ While the ACS reports geography at the levels of census tracts, counties, and st
 - Employment rate of a ZIP code is defined as the percentage of the residing population who are employed as a part of the civilian labor force;
 - Income measure of a ZIP code is defined as the average value of tract-level median household income in the past 12 months, weighted by tract population counts;
 - ADI of a ZIP code is the average ADI across covered census tracts, weighted by tract population counts.
-ß
+
 Code reference: [combine_tracts_covid](https://github.com/mrp-interface/shinymrp/blob/main/dev/scripts/create_data.R#L97).
 
 ### Poststratification tables

vignettes/method.Rmd

@@ -43,13 +43,13 @@ where $e_s$ is a ZIP-code-level random error.
 
 The interface allows users to specify alternative priors, including structured priors for high-order interaction terms developed by [Si et al. (2020)](https://www150.statcan.gc.ca/n1/en/pub/12-001-x/2020002/article/00003-eng.pdf?st=iF1_Fbrh).
 
-Because the outcome model assumes that the people in the same poststratification cell share the same response probability, we can replace the microdata with cellwise aggregates and employ a binomial model for the sum of the responses in cell $j$ as $y^*_j \sim \textrm{binomial}(n_j, \theta_j)$, where $n_j$ is the sample cell size and $\theta_j=\textrm{logit}^{-1}(
+Because the outcome model assumes that the people in the same poststratification cell share the same response probability, we can replace the microdata with cell-wise aggregates and employ a binomial model for the sum of the responses in cell $j$ as $y^*_j \sim \textrm{binomial}(n_j, \theta_j)$, where $n_j$ is the sample cell size and $\theta_j=\textrm{logit}^{-1}(
 \beta_1+\beta_2{\rm male}_j +
 \alpha_{\rm a[j]}^{\rm age}
 + \alpha_{\rm r[j]}^{\rm race}
 + \alpha_{\rm s[j]}^{\rm ZIP}
 )
-$ using the cellwise effects of all factors. The interface thus allows users to upload microdata or cellwise aggregates as the input data. 
+$ using the cell-wise effects of all factors. The interface thus allows users to upload microdata or cell-wise aggregates as the input data. 
 
 To generate overall population or subgroup estimates, we combine model predictions within the poststratification cells---in the contingency table of sex, age, race, and ZIP---weighted by the population cell frequencies $N_j$, which are derived from the linked ACS data in our application. Additionally, users may choose to upload custom poststratification data for specific target populations (e.g., a different country, rather than the U.S.). If we write the expected outcome in cell $j$ as $\hat{\theta}_j$ in cell $j$, the population average from MRP is then:
 $$
@@ -67,7 +67,7 @@ When the outcome is continuous, we specify linear regression models and estimate
 
 As an example of time-varying data, we model weekly PCR testing results. We use a Bayesian framework to account for the PCR testing sensitivity and specificity. Here, MRP proceeds in two steps: (1) fit a multilevel model to the testing data for incidence incorporating time and covariates, and (2) poststratify using the population distribution of the adjustment variables: sex, age, race, and ZIP codes, where we assume the population distribution is the same during the study period. Hence, the poststratification cell is defined by the cross-tabulation of sex, age, race, ZIP code, and indicators of time in weeks based on the test result dates.
 
-We denote the PCR test result for individual $i$ as $y_i$, where $y_i=1$ indicates a positive result and $y_i=0$ indicates negative. Similarly, with poststratification cells, we assume that people in the same cell have the same infection rate and can directly model cellwise summaries. We obtain aggregated counts as the number of tests $n_j$ and the number of positive cases $y^*_j$ in cell $j$. Let $p_j=\textrm{Pr}(y_{j[i]}=1)$ be the probability that person $i$ in cell $j$ tests positive. We account for the PCR testing sensitivity and specificity, where the positivity $p_j$ is a function of the test sensitivity $\delta$, specificity $\gamma$, and the true incidence $\pi_j$ for people in cell $j$:  
+We denote the PCR test result for individual $i$ as $y_i$, where $y_i=1$ indicates a positive result and $y_i=0$ indicates negative. Similarly, with poststratification cells, we assume that people in the same cell have the same infection rate and can directly model cell-wise summaries. We obtain aggregated counts as the number of tests $n_j$ and the number of positive cases $y^*_j$ in cell $j$. Let $p_j=\textrm{Pr}(y_{j[i]}=1)$ be the probability that person $i$ in cell $j$ tests positive. We account for the PCR testing sensitivity and specificity, where the positivity $p_j$ is a function of the test sensitivity $\delta$, specificity $\gamma$, and the true incidence $\pi_j$ for people in cell $j$:  
 \begin{align}
 \label{positivity}
 p_j=(1-\gamma)(1-\pi_j )+\delta \pi_j.

vignettes/workflow.Rmd

@@ -8,7 +8,7 @@ vignette: >
 ---
 
 
-This vignette provides an in-depth walkthrough of the `MRPWorkflow` and `MRPModel` classes in the **shinymrp** package. You will find practical information about the purpose, arguments, and caveats of each method, enabling you to conduct MRP analyses programmatically.
+This vignette provides an in-depth walk-through of the `MRPWorkflow` and `MRPModel` classes in the **shinymrp** package. You will find practical information about the purpose, arguments, and caveats of each method, enabling you to conduct MRP analyses programmatically.
 
 For an introduction to the package and workflow concepts, begin with the [Getting started with shinymrp](https://mrp-interface.github.io/shinymrp/articles/getting-started.html) vignette.