# Modeling a repeated measures growth curve

I have cumulative population totals data for the end of each month for two years (2016, 2017). I would like to combine these two years and treat each months cumulative total as a repeated measure (one for each year) and fit a non linear growth model to these data. The goal is to determine whether our current 2018 cumulative monthly totals are on track to meet our higher 2018 year-end population goal by increasing the model's asymptote to our 2018 year-end goal. I would ideally like to integrate a confidence interval into the model that reflects the variability between the two years at each month.

My columns in my data.frame are as follows: - Year is year - Month is month - Time is the month's number (1-12) - Total is the month-end cumulative population total - Norm is the proportion of year-end total for that month - log is the Total log transformed Year Month Total Time Norm log 1 2016 January 3919 1 0.2601567 8.273592 2 2016 February 5887 2 0.3907993 8.680502 3 2016 March 7663 3 0.5086962 8.944159 4 2016 April 8964 4 0.5950611 9.100972 5 2016 May 10014 5 0.6647637 9.211739 6 2016 June 10983 6 0.7290892 9.304104 7 2016 July 11775 7 0.7816649 9.373734 8 2016 August 12639 8 0.8390202 9.444543 9 2016 September 13327 9 0.8846920 9.497547 10 2016 October 13981 10 0.9281067 9.545455 11 2016 November 14533 11 0.9647504 9.584177 12 2016 December 15064 12 1.0000000 9.620063 13 2017 January 3203 1 0.2163458 8.071843 14 2017 February 5192 2 0.3506923 8.554874 15 2017 March 6866 3 0.4637622 8.834337 16 2017 April 8059 4 0.5443431 8.994545 17 2017 May 9186 5 0.6204661 9.125436 18 2017 June 10164 6 0.6865248 9.226607 19 2017 July 10970 7 0.7409659 9.302920 20 2017 August 11901 8 0.8038501 9.384378 21 2017 September 12578 9 0.8495778 9.439705 22 2017 October 13422 10 0.9065856 9.504650 23 2017 November 14178 11 0.9576494 9.559447 24 2017 December 14805 12 1.0000000 9.602720

Here is my data plotted as a scatter plot:

Should I treat the two years as separate models or can I combine all the data into one?

I've been able to calculate the intercept and the growth parameter for just 2016 using the following code: coef(lm(logit(df_tot$Norm[1:12]) ~ df_tot$Time[1:12]))

and got a non-linear least squares regression for 2016 with this code: fit <- nls(Total ~ phi1/(1+exp(-(phi2+phi3*Time))), start = list(phi1=15064, phi2 = -1.253, phi3 = 0.371), data = df_tot[c(1:12),], trace = TRUE)

Any help is more than appreciated! Time series non-linear modeling is not my strong suit and googling hasn't got me very far at this point.