chemdeg is a package developed to assist food chemists in the objective selection of degradation kinetic models of foods and parameters estimation. The software implements a two-step method to this purpose. First, experimental data are analyzed in the so-called phase space which allows for the estimation of the order of the reaction; then the data are fitted with the appropriate standard kinetic model to estimate the reaction rate. The whole procedure is driven by rigorous statistical analyses of the results. The package also provides a routine to fit a non-standard kinetic degradation model named first-order multi-target model (FOMT).

You can install the development version of chemdeg like so:

```
# from CRAN
install.packages("chemdeg")
# from GitHub
library(devtools)
::install_github("migliomatte/chemdeg",
devtoolsdependencies = TRUE, build_vignettes = TRUE)
```

`library(chemdeg)`

The determination of the reaction order of a generic degradation
kinetic model is often prone to subjectivity. By analyzing the phase
space of the kinetic system it is possible to statistically determine
the reaction order. This information can then be used to determine the
reaction rate constant. In the package `chemdeg`

the whole
analysis can be performed with the function
`det_order()`

:

```
<- det_order(ord1)
res #> Reaction order estimated: 1
```

where `ord1`

is a built in function for
1^{st}-order kinetic model data.

The function `results`

returns statistics and parameters
estimates:

```
results(res)
#>
#> Linear regression in the phase space:
#> log(dx/dt)= 0.97 log(x) + ( -0.46 )
#>
#> Estimate of n:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> 9.701806e-01 4.235714e-03 2.290477e+02 1.835114e-07
#>
#> Confidence interval of n:
#> 2.5 % 97.5 %
#> 0.9567007 0.9836605
#>
#> Statistical analysis indicates that an order 1 degradation kineitc model is likely to describe the data.
#> The null hypothesis H0:
#> "The process is described by an order 1kinetic model"
#> cannot be rejected.
#>
#> Non-linear least squares regression was performed with an order 1 kinetic model:
#>
#> Estimate of k:
#> Estimate Std. Error t value Pr(>|t|)
#> k 0.6878765 0.002626997 261.8489 1.541636e-11
#> In attesa che venga eseguita la profilazione...
#> Confidence interval of k:
#> 2.5% 97.5%
#> 0.6812276 0.6947116
#>
#> Goodness-of-fit:
#> Value
#> AIC: -11.933893
#> AICc: -10.933893
#> BIC: -12.350374
#> RMSE: 2.002812
#> Chi-sq_red: 5.379602
#> -----------------------------------------------------
```

Plots of the data in both the phase space and the normal
concentration vs time space along with their best fits with model
equations can be accessed with `plot_ord()`

:

`plot_ord(res)`

The following is an example of first-order multi-target (FOMT) model.
The `FOMT()`

function can be used to perform the fit:

```
<- FOMT(fomtdata)
fit_fomt summary(fit_fomt)
#>
#> Formula: y ~ 1 - (1 - exp(-k * t))^n
#>
#> Parameters:
#> Estimate Std. Error t value Pr(>|t|)
#> k 0.056836 0.008206 6.926 0.000449 ***
#> n 9.478174 3.926148 2.414 0.052280 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.04243 on 6 degrees of freedom
#>
#> Number of iterations to convergence: 10
#> Achieved convergence tolerance: 3.98e-06
```

where `fomtdata`

is an example data-frame provided with
the package.

If the `FOMT()`

function does not converge, it is possible
to use the `nls`

function from `stats`

package as
follows:

```
<- nls(y ~ FOMTm(t, k, n),
fit_fomt1 data = list(y = fomtdata$tCQA_AA, t = fomtdata$time_h),
start = list(n = 10, k = 0.05)
)summary(fit_fomt1)
#>
#> Formula: y ~ FOMTm(t, k, n)
#>
#> Parameters:
#> Estimate Std. Error t value Pr(>|t|)
#> n 9.478163 3.926141 2.414 0.052280 .
#> k 0.056836 0.008206 6.926 0.000449 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 0.04243 on 6 degrees of freedom
#>
#> Number of iterations to convergence: 9
#> Achieved convergence tolerance: 5.453e-06
```

`chemdeg`

implements the chi-squared reduced statistics
(\(\chi^2_{red}=\chi^2/df\) where \(df\) are the degrees of freedom) and the
Akaike Information Criterion with correction for small sample size
(AICc) as goodness of fit measures. These can be accessed with the
functions `chiquad_red()`

and `AICC()`

,
respectively.

To access the full table comprising the Bayesian Information
Criterion (BIC), Akaike Information Criterion (AIC), AICc, Root Means
Squared Error (RMSE) and \(\chi^2_{red}\) (from both package
`stats`

and `chemdeg`

) call the function
`goodness_of_fit()`

:

```
goodness_of_fit(fit_fomt)
#> Value
#> AIC: -24.15681095
#> AICc: -21.75681095
#> BIC: -23.91848633
#> RMSE: 0.04243006
#> Chi-sq_red: NA
```

For more details see

`vignette("chemdeg_basics","chemdeg")`