# Growth fitting considering link between mu and lambda for the Baranyi-Ratkowsky model This function implements the methodology suggested by Garre et al. (2025; doi: 10.1016/j.ijfoodmicro.2025.111078) for the Baranyi-Ratkowsky model. Rather than fitting independent models for mu and lambda, this approach considers a link between both secondary models, reducing the number of unknown parameters from 3 to 4. The function implements too modes of fitting: two-steps and one-step. Please see the respective sections for further information. ```r fit_coupled_growth( fit_data, start, known = c(), mode = "two_steps", weight = "sd", ..., logbase_mu = exp(1), logbase_logN = 10 ) ``` ## Arguments - `fit_data`: a tibble (or data.frame) with the data for the fit. The content must be different depending on the fitting mode (see relevant sections within the help page). - `start`: a numeric vector of initial guesses for the parameter estimates - `known`: a numeric vector of known mode parameters. An empty vector by default (no knonw parameter) - `mode`: the type of model fitting approach. Either `two_steps` (fitted from the values of `mu` and `lambda`) or `one_step` (fitted from logN) - `weight`: weights to apply for the `two_steps` fit. Either `NULL` (no weights), `sd` (standard deviation; default) or `mean` (mean value). - `...`: ignored - `logbase_mu`: Base for the definition of mu. By default, `exp(1)` (natural logarithm). - `logbase_logN`: Base for the definition of logN. By default, 10 (decimal logarithm). ## Two-steps fitting In this mode, it is assumed that primary models have been already fitted to each experiment. Therefore, the data is available as a table of values of mu and lambda estimated at each temperature. Hence, `fit_data` must be a tibble (or data.frame) with three columns: `temp` (storage temperature), `mu` (specific growth rate) and `lambda` (lag phase duration). By default, `mu` must be defined in the scale of natural logarithm, although this can be modified using the `logbase_mu` argument. The package includes the dataset `example_coupled_twosteps` as an illustration of the type of data. ## One-step fitting In this mode, secondary models are directly fitted to the observed (log) microbial counts. Hence, `fit_data` must be a tibble (or data.frame) with three columns: `temp` (storage temperature), `time` (the elapsed time) and `logN` (the log-microbial concentration). By default, `logN` must be defined in the scale of decimal logarithm, although this can be modified using the `logbase_logN` argument. The package includes the dataset `example_coupled_onestep` as an illustration of the type of data. ## Examples ```r ## Example 1: Two-steps fitting------------------------------------------------- ## We can use the example dataset data(example_coupled_twosteps) ## We need to define initial guesses for every parameter guess <- c(logC0 = -1, b = .1, Tmin = 5) ## We can now call the fitting function my_fit <- fit_coupled_growth(example_coupled_twosteps, start = guess, mode = "two_steps") ## Common S3 methods are included print(my_fit) coef(my_fit) summary(my_fit) plot(my_fit) ## Any model parameter can be fixed using the known argument known <- c(b = .01) ## Please note that the guess must be updated, as now parameter can appear both as a guess and known guess <- c(logC0 = -1, Tmin = 0) fixed_fit <- fit_coupled_growth(example_coupled_twosteps, start = guess, known = known, mode = "two_steps") print(fixed_fit) coef(fixed_fit) summary(fixed_fit) plot(fixed_fit) ## Example 2: One-step fitting-------------------------------------------------- ## We can use an example dataset with the right format data("example_coupled_onestep") ## The function requires initial guesses for every model parameter guess <- c(logN0 = 2, logNmax = 8, b = 0.04, logC0 = -4, Tmin = 5) ## We can now call the fitting function my_fit <- fit_coupled_growth(example_coupled_onestep, start = guess, mode = "one_step") ## The package includes common S3 methods print(my_fit) coef(my_fit) summary(my_fit) plot(my_fit) ## Any model parameter can be fixed before fitting known <- c(logNmax = 7) ## Guesses must be updated, so no parameter appears twice guess <- c(logN0 = 2, b = 0.04, logC0 = -4, Tmin = 5) ## We can now call the fitting function my_fit <- fit_coupled_growth(example_coupled_onestep, start = guess, known = known, mode = "one_step") ## The package includes common S3 methods print(my_fit) coef(my_fit) summary(my_fit) plot(my_fit) ```

fit_coupled_growth function