Interval Specific Rate Parameter (ISRP)
Growth curve models play an instrumental role in quantifying the growth of biological processes and have immense practical applications across disciplines. Relative growth rate (RGR), devised by Fisher (1921), is the most popular measure of growth, by assuming exponential growth between two consecutive time points. RGR remains invariant under any choice of the underlying growth model. Bhowmick et al. (2014) proposed the concept of Modified RGR which is a model-specific formula for RGR. The authors have introduced the concept of ISRP to derive the modified RGR and have shown that the use of Modified RGR is advantageous as compared to Fisher’s RGR in selecting the best model for real data sets (Pal et al., 2018). The idea of ISRP has been further extended to develop an efficient way of selecting the best model from a set of nonlinear growth equations (Karim et al., 2022). The key point about ISRP is that it can detect the crucial interval where the growth is erratic and unusual. Model selection using ISRP has been used by many researchers (Crescenzo and Spina, 2016; Asadi et al., 2020). Using the concept of ISRP one can also detect the parameter variation from real data. Successful applications of ISRP have already been demonstrated in population growth, market research, and epidemiology (Karim et al., 2022).
Here, we will demonstrate the derivation of ISRP by using Bhowmick et al. (2014)'s method in R software.
References:
Fisher R.A.,1921. Some remarks on the methods formulated in a recent article on “the quantitative analysis of plant growth. Ann Appl Biol; 7(4):367–72.
Bhowmick A.R., Chattopadhyay G., Bhattacharya S., 2014. Simultaneous identification of growth law and estimation of its rate parameter for biological growth data: a new approach. J Biol Phys; 40(1):71–95.
Pal A., Bhowmick A.R., Yeasmin F., Bhattacharya S., 2018. Evolution of model specific relative growth rate: its genesis and performance over fishers growth rates. J Theor Biol; 4 4 4:11–27.
Karim, M.A.U., Bhagat, S.R., Bhowmick, A.R., 2022. Empirical detection of parameter variation in growth curve models using interval specific estimators. Chaos Solitons Fractals (ISSN: 0960-0779) 157, 111902.
Crescenzo A.D., Spina S., 2016. Analysis of a growth model inspired by Gompertz and Korf laws, and an analogous birth-death process. Math Biosci; 282:121–34.
Asadi M., Di Crescenzo A., Sajadi F.A., Spina S., 2020. A generalized Gompertz growth model with applications and related birth-death processes. Ric Mat:1–36.