Model that switches between exponential equations based on state variable

[Rob Henst]

Hi Statalists,

I have a problem that is more mathematical than Stata-related. I know this is a long shot, but I have to try.

• I am calculating a score (HS) which runs on a scale from 0% to 100%.
• HS should increase exponentially while state == 1.
• HS should decrease exponentially while state == 0
• HS should be 100% if state == 1, 91 t in a row. In other words if state == 1 for t1 to t91 (meaning the sum of state = 91), HS should be 100%.

I have the equation which works if state == 1 for t1 to t91, and I have the equation which decreases exponentially from 100% to 0% while state == 0 for t1 to t91.

Just for context, t = one day, and the 91 represents 3 months (365 / 12 * 3). The state refers to an occurrence that did (1) or did not (0) happen that day. If the occurrence happens 91 days in a row, HS must be 100%.

I don't know how to explain my problem better - which is probably why I haven't been successful finding a solution via Google.

Code if state == 1 for t1 to t91:

clear
insobs 91
egen t = seq()
gen state = 1
gen hs = (state*t^2)/(91^2)*100
twoway (line hs t)

Code if state == 0 for t1 to t91:

clear
insobs 91
egen t = seq()
gen state = 0
gen hs = (91^2-(-t-(1))^2)/(91^2)*100
twoway (line hs t)

In the end, the data, when plotted, should look something like this, assuming a period where state ==1, followed by a period where state ==0, followed by a period where state == 1 again:

Thank you so much in advance.

[Clyde Schechter]

Would this serve your purposes?

clear*
set obs 91

gen int t = _n
sort t

//  SAMPLE CASES
gen state1 = 1 // SHOULD RISE TO 100%

gen state2 = (t < 60 | t > 80) // SHOULD RISE TO PEAK AT 60, FALL, THEN RISE AFTER 80

gen state3 = 0

forvalues i = 1/3 {
    gen cum_state`i' = (sum(state`i' == 1) - sum(state`i' == 0))/t
    gen hs`i' = max(100*(cum_state`i'*t^2)/(91^2), 0)
}

graph twoway line hs* t, sort

By the way, your code suggests that you do not intend to have exponential evolution of hs, as your code uses a quadratic function. In fact, you can't have exponential change because an exponential can never be zero.

[Rob Henst]

Thanks a lot, Clyde.

That serves my purpose.

Thank you for pointing out my equation is quadratic and not exponential. I will look into that later.