norm_sim: Simulate Growth paths based on norms tables
In almartin82/MAP-visuals: KIPP MAP Visuals

Description Usage Arguments Details Value Examples

norm_sim simulates n.samples student growth paths using the mean and standard deviation estimates provided in NWEA's 2011 Student Growth Norms data tables.

1 2	norm_sim(start.grade = 5, end.grade = 8, start.subject = "Mathematics", start.rit = 190, yearly.cycle = c(41, 12), n.samples = 5000)

`start.grade`	start grade as integer
`end.grade`	end grade as integer
`start.subject`	measurement scale
`start.rit`	starting RIT value as integer for simulation
`yearly.cycle`	season intervals used to identify typical growth and standard deviations. These are passed as a vector of two digit intergers in the style of the 2011 Student Growth Norms Table where each season recieves an integer value corresponding to Winter = 1, Spring = 2, Fall = 4. Integer pairs indicate the appropriate interval to simulate growth. For example, to simulate fall-to-winter followed by winter-to-spring growth for each grade level the vector `c(41,12)` is passed to this paramter (this is the default behavior of the function). Here 41 indicates fall-to-winter growth and 12 indicates winter-to-spring.
`n.samples`	the number of samples

This function builds a growth path over specified intervales (e.g., spring-to-spring, fall-to-winter followed by winter-spring) as well as grades (eg. 5-8, K-11) for a given start grade, measurement scale (i.e., subject) and starting RIT value. All simulations start wiht the same RIT value and then iterativelydraw the next assessments realization from rnorm using the means and standard deviations for appropriate intervals as provided by the norms_student_2011. The function iterates over grades and intervals within grades and construct a data.table in long format.

a data frame with n.sample + (n.sample x grades x length(yearly.cycle) rows).

# Run simulations with defaul settings
x.t <- norm_sim()

# Create grade-season variable for summary stats and plotting
x.t[,GradeSeason:=ifelse(Season==41, StartGrade-.7, StartGrade)]

# Calculate grade-season means
x.avg<-x.t[,list(Avg=mean(StartRIT), sigma=sd(StartRIT)), by=list(GradeSeason)]

# Calculate grade-season upper and lower confidence levels
x.avg[,ucl:=Avg+1.96*sigma]
x.avg[,lcl:=Avg-1.96*sigma]

# Plot!
p <- ggplot(x.t, aes(x=GradeSeason, y=StartRIT))  + geom_line(aes(group=ID), alpha=.01) + theme_bw()
p + geom_smooth(data=x.avg, aes(x=GradeSeason, y=Avg, ymin=lcl, ymax=ucl), color="orange", fill="orange", size=1.7)