Example-Analysis

Morefi: Example Analysis

This a methodological package developed in R. It includes functions that support data analysis and ensure reproducibility of the results reported in the article by Aguirre-Villaseñor et al. (2025).

In fisheries monitoring, body length is the most commonly measured parameter because it is quick and easy to obtain. In contrast, measuring weight requires a level and stable scale, which can be difficult to secure in field sampling. Biometric relationships are crucial in fisheries biology. When accurately calculated, these relationships can be very useful for management purposes, especially for estimating an organism’s total length or weight based on other body measurements.

Many species are marketed through artisanal fishing in various commercial forms. However, there are currently no biometric relationships that allow for predicting live weight (the total weight of the fish) from the different categories of landed weight, such as fillet weight, gutted weight, or frozen weight.

The objective of this package is to provide quantitative analysis for various morphological relationships that help predict: a) the expected live weight of different landed weight categories, b) the expected fillet yield from various commercial presentations, and c) testing the suitability of fillet yield as a reference point in managing the target species.

For this purpose, some functions and a vignette were created to explain the process step by step. Its implementation streamlines the methodology and enhances the clarity and impact of both the results and graphical presentations (tables and figures are personalized).

The functions included in the Morefi package enable the evaluation of length-length, weight-weight and length-weight biometric relationships using data that exhibit high variability and do not meet the assumptions necessary for adjustment via least squares. Given this variability, a robust regression method is employed for analysis. The “robustbase” package (version 0.99-2) was utilized to fit robust regression models, using the functions lmrob() for linear and nlrob() for non-linear regression (Maechler et al., 2024).

Installation

You can install the development version of Morefi from GitHub using one of the following options:

Using the pak package

# install.packages("pak")
pak::pak("Macrurido/Morefi")

or using the devtools package

library(devtools)
install_github("Macrurido/Morefi")

Data available in the package

The package contains two data sets. Data are available under the terms of the The Creative Commons Attribution 4.0 International (CC BY 4.0).

Bullseye puffer measures

To demonstrate how the package functions, we utilize the dataset botete, containing 1,397 fish across 7 variables: the total length(LT), standard length (SL), body trunk length (LB), total weight (WT), body trunk weight (WB), fillet weight (Wfi) and Fleet of the bullseye puffer (Sphoeroides annulatus), collected from the Eastern Central Pacific. In this dataset, the landing category is included in the “Fleet” variable, which is categorized as follows: 1 indicates Fresh, while 2 denotes Frozen-thawed. This biometric data file, is included in the package with permission from the Instituto Mexicano de Investigación en Pesca y Acuacultura Sustentables (Mexican Institute for Research in Sustainable Fishing and Aquaculture).

To access the data file, the data frame is stored in an object, such as ‘mydata’.

mydata <- Morefi::Botete
str(mydata)
#> 'data.frame':    1397 obs. of  7 variables:
#>  $ LT   : num  21 22 12 21 12 28.4 29.3 34.8 31.7 31.5 ...
#>  $ LS   : num  17.3 17.6 10 17.3 10 23 24.2 27.5 25.5 26 ...
#>  $ LB   : num  17 15 10 15 8.5 20 20.5 27 23 24 ...
#>  $ WT   : num  189.1 213.4 33.4 236.7 36 ...
#>  $ WB   : num  115.6 86.7 15.4 100.4 18.9 ...
#>  $ Wfi  : num  50.7 55.5 6.9 65 9.1 ...
#>  $ Fleet: Factor w/ 2 levels "1","2": 2 2 2 1 2 1 2 1 1 1 ...

Bullseye puffer fish landings

A second dataset Botete_land, provided the Mexican fishing records of bullseye puffer landed on the Pacific coast in 2023 and their live weight corresponding live weight for each weight category (kg): total (WT), body trunk (WB) or fillet (Wfi), either Fresh or Frozen-thawed (SIPESCA, 2024).

To access the data file, the data frame is stored in catch.

catch <- Morefi::Botete_land
catch
#>          Category  Landed   Biomass    Pesos  Pesos_kg
#> 1        WT_Fresh  509354  509354.0  33079.5  41.49873
#> 2        WB_Fresh  449646  494610.6  58048.0  52.05232
#> 3 WB_Fresh_Thawed  361404  451755.0  37997.0  54.77369
#> 4       Wfi_Fresh   47990   95980.0  16485.0 112.83715
#> 5           Total 1368394 1551699.6 145609.5  50.97446

theme_papers()

The theme_papers() is created to standardize the graphic format, used as base theme_bw(). To showcase their design, this manual presents graphics in both their original format and the format created using the theme_papers().

To call the theme_papers() function use the following statement:

theme_papers <- Morefi::theme_papers()

Values to define for the examples

Esto no lo se Rick

The following objects, data frames, and lists will be utilized in multiple examples to avoid repetition of information.

List: modelos

A list that defines the variables that will be taken into account for the model.

modelos <- list (LTvs.LS  =  c(1,2),
                 LTvs.WT  =  c(1,4))

Morefi functions

The Morefi package includes functions that facilitate data analysis and ensure reproducibility of results. The functions for analysis are outlined below, followed by the functions for plotting.

Analysis functions

fn_ARSS()

The function fn_ARSS() perform the Coincident Curves Test, to determine if there are significant differences between the fitted curves for each database. It is based on the Analysis of the Residual Sum of Squares (ARSS) (Chen et al. 1992).

$F=\frac{\frac{RSS_{p}-RSS_{s}}{3\bullet \left( K-1 \right)}}{\frac{RSS_{s}}{N-3\bullet K}}$

$RSS_{p}= RSS$ of each regression fitted by pooled data, $RSS_{s}$ = sum of the $RSS$ of each regression fitted for each individual sample, $N$ = total sample size, and $K$ = number of samples in the comparison.

The residual sum of squares $RSS$ and the degrees of freedom $DF$ for each fitted regression are previously stored in the List_TCCT list. For each regression, the calculations are stored in a data frame T1, which is stored iteratively using a loop for in a list T.

Inside the function, the RSS and DF for the joined sample are calculated to perform the F test for two tails $\alpha/2$ . The decision criteria is performed: “*” if $p-value\le \alpha$ or “NS” if the $p-val\gt \alpha$ .

The function requires defining:

List_TCCT: A list with fitted regression results.
i: An integer value indicating the ith regression analyzed.
alfa: A numerical value that defines the significance level. The default number is 0.05.

The function return a data frame containing the results of the Coincident Curves Test stored in a list.

Example

The Total length (LT) - Total weight (WT) was estimated for the bullseye puffer Sphoeroides annulatus for landed categories: Fresh, Frozen-thawed (Frozen), Total (All sample) and Joined (sum of values of Fresh and Frozen). The Residual Sum of Squares (RSS) and the degrees of freedom (DF) are provided for each data source. In the table the first row displays the Analysis of Residual Sum of Squares (ARSS), the p-value (p), and the decision criteria for the ARSS test (Criteria).

In the table the first row displays the Analysis of Residual Sum of Squares (ARSS), the p-value (p), and the decision criteria for the ARSS test (Criteria).

The adjusted models show the following data: Fresh SSR= and DF= 742; Frozen SSR= 1280131.81 and DF= 651; and the total sample SSR= 6115874.53 and DF= 1395. Values are stored in the table Table_CC, this is stored in a list, and the name of each item is built with the acronyms of the model variables (e.g. LTWT).

Table_CC <- data.frame(matrix(NA,nrow=4,ncol=8))
Table_CC[1,1] <- "Lt-WT" 
Table_CC[,2] <- c("Fresh","Frozen","Total","Joined")
colnames(Table_CC) <- c("Model","Category","RSS","DF","ARSS","F-table","p-value","Criteria")

Table_CC[1,3] <- 4424418.33
Table_CC[1,4] <-  742 
Table_CC[2,3] <- 1280131.81
Table_CC[2,4] <-  651 
Table_CC[3,3] <- 6115874.53
Table_CC[3,4] <-  1395 

List_ARSS <- list(LTWT=Table_CC)

i <- 1

ARSS <- fn_ARSS(List_ARSS, i,  alfa= 0.05)

Table of the Coincident Curve Test.
Model	Category	RSS	DF	ARSS	F-table	p-value	Criteria
LT vs. WT	Fresh	4424418	742	0.0721	1.0921	0.05007	NS
NA	Frozen	1280132	651	NA	NA	NA	NA
NA	Total	6115875	1395	NA	NA	NA	NA
NA	Joined	5704550	1393	NA	NA	NA	NA

ⓘ To enhance the visualization of the function results, tables and their headers were constructed using the knitr and kableExtra packages. The code is not displayed.

fn_dfa()

This function uses the augment() function from the broom package to extract the observed values of the independent variable (x) and dependent variable (y), along with the weights (wi), fitted values (fitt), and residuals (ei) from the summary of the fitted model. It then turns these components into tidy tibbles.

The function augment() does not provide the weights column for the lmrob() function. The function fn_dfa() contains a conditional statement that includes this variable in the output data frame of the linear adjustments.

In order to homogenizes the results, the columns names were renamed as “y”, “wi”,“x”,“fitt”,and “ei”.

An additional column has been included that codes errors using a scale based on weighted values: unweighted (u), weighted (w), and outliers (o) dfa$scale <- ifelse(df$wi < 0.25, "o", ifelse(df$wi<1, "w", "u")).

The function requires defining:

eq: Summary of the equation fitted.

Example

Using the biometric data from Morefi::botete, a linear relationship between Total Length and Standard Length (LT_LS) was established using the robustbase::lmrob function. Additionally, the relationship between Total Length and Total Weight (LT_WT) was fitted using the robustbase::nlm function, with an input y-value of a = 0.1 and a slope of b = 3.

For optimal functionality of fn_dfa(), the data frames used for fitting relationships must be formatted as tibble.

library(dplyr)
library(tibble)

df <- dplyr::tibble(x1 = mydata[,1],
                y1 = mydata[,2])

eq1 <- robustbase::lmrob(y1 ~ x1, data= df,
                                  setting = "KS2014",
                                              doCov = TRUE)
dfa1 <- fn_dfa(eq= eq1)

#  Power Model
df <- dplyr::tibble(x1 = mydata[,1],
                y1 = mydata[,4])

a=0.01
b=3

eq2 <- robustbase::nlrob(y1 ~ a*x1^b, data= df,
                        start = list(a= a, b= b),
                        trace = FALSE)

dfa2 <- fn_dfa(eq= eq2)

The first six rows of the table are displayed, based on the LT versus LS relationship results.
y	x	fitt	ei	wi	scale
17.3	21.0	17.174230	0.1257696	1.0000000	u
17.6	22.0	17.999109	-0.3991088	0.9914912	w
10.0	12.0	9.750324	0.2496758	1.0000000	u
17.3	21.0	17.174230	0.1257696	1.0000000	u
10.0	12.0	9.750324	0.2496758	1.0000000	u
23.0	28.4	23.278331	-0.2783310	1.0000000	u

The first six rows of the table are displayed, based on the LT versus WT relationship results.
y	wi	x	fitt	ei	scale
189.1	1.0000000	21.0	209.81549	-20.71549	u
213.4	1.0000000	22.0	242.19890	-28.79890	u
33.4	1.0000000	12.0	37.32321	-3.92321	u
236.7	1.0000000	21.0	209.81549	26.88451	u
36.0	1.0000000	12.0	37.32321	-1.32321	u
457.0	0.5098231	28.4	532.50610	-75.50610	w

ⓘ To enhance the visualization of the function results, tables and their headers were constructed using the knitr and kableExtra packages. The code is not displayed.

fn_freq()

It is used as an internal function within fn_freqw().

The fn_freq() function calculates a frequency distribution of data using the cut() and table() functions from the R base. It produces a data frame that displays frequencies categorized by class interval.

Within the function, the non-cumulative absolute frequency is calculated for each user-defined class interval based on the breaks object. The breaks object must be defined outside the function by the user.

The attributes and examples of fn_freq() are detailed in the documentation for the fn_freqw() function below.

See also cut() and table() from the R base package.

fn_freqw()

The fn_freqw() calculate the percentage frequencies of weights by model adjusted using the robust regression approach. The function calculates the relative frequency distribution using the function fn_freq() from Morefi package. It returns a table with frequencies by class interval.

The breaks object must be defined. To incorporate the number of non-weighted values $(w_{i}=1)$ , a class interval “1” is added to the sequence inside the function.

The function requires defining:

df A vector of data values.
breaks A vector with class intervals.
right Logical, indicating if the intervals should be closed on the right (and open on the left) or vice versa.

See also Morefi::fn_freq; cut() and table() from the R base package.

Example

The weighted values were obtained from the summary of linear and power models fitted using robust regression and stored in dfa1 and dfa2, which were generated with the fn_dfa() example. In each data frame, the weighted values are stored in the column labeled “wi.”

The function fn_freqw() calculates the frequency of weighted values within a defined interval based on a weighted scale classification: unweighted $(w_{i}=1)$ , weighted $(1>w_{i}≥0.25)$ , and outliers $(w_{i}<0.25)$ . The weighted scale is stored in breaks.

breaks  <-  c(0,0.25,1,Inf) # Weighted scale

df <- dfa1$wi    # Data frame 1
freq1 <- fn_freqw(df, breaks, right=FALSE)

df <- dfa2$wi    # Data frame 2
freq2 <- fn_freqw(df, breaks, right=FALSE)

# Merging the two data sets (as example) 
freqw <- as.data.frame(t(cbind(freq1, freq2)))

Percentage frequencies of weights (wi) based on a weighted scale classification
	[0,0.25)	[0.25,1)	[1,Inf)
freq1	1.216893	30.06442	68.71868
freq2	3.364352	27.05798	69.57767

ⓘ To enhance the visualization of the function results, tables and their headers were constructed using the knitr and kableExtra packages. The code is not displayed.

fn_xseq()

The function creates a data frame containing a sequence for the selected independent variable based on the model. The lower end of the range is determined by rounding down the minimum value to the nearest multiple of the specified “bin” step size, while the upper end is determined by rounding up the maximum value.

The data frame should have the same column name as the dependent variable used in the fitted model.

The function requires defining:

df A data frame includes the morphological variables.
modelos A list defining the numerical column variables for the model.
bin A vector contains the step size for each independent variable in every model.
i An integer value indicating the regression to be analyzed.

The function returns a one-column data frame with the sequence selected.

Example

Using biometric data from Morefi::botete, the sequence of independent variables for the relationships between Total Length and Standard Length (LT_LS) and between Total Length and Total Weight (LT_WT) was computed using the function fn_xseq.

The object modelos was defined earlier in the section titled Values to Define for the Examples.

df <- mydata
bin <- c(2)
i=1
xseq1 <- fn_xseq(df, modelos, bin, i)

bin <- c(5)
i=2
xseq2 <- fn_xseq(df, modelos, bin, i)

The first nine columns of the table are displayed, based on the sequence of independent variables for the relationships between Total Length and Standard Length (LT_LS), and between Total Length and Total Weight (LT_WT).
	1	2	3	4	5	6	7	8	9
x1	8	10	12	14	16	18	20	22	24
x1	5	10	15	20	25	30	35	40	45

ⓘ To enhance the visualization of the function results, tables and their headers were constructed using the knitr and kableExtra packages. The code is not displayed.

fn_intervals()

The function calculates a non-parametric confidence and predicted intervals using the function predFit() from the package investr (version 1.4.2).

The function requires defining:

xseq A vector with a sequence for independent variable.
eq Summary of the equation fitted.

The function return a data frame df with the xseq (x1), the fitted values for dependent variable (fit), the low and upper confident (IC_L and IC_U) and predicted intervals (IP_L and IP_U).

Example


eq <- eq1
xseq <- xseq1
CI <- fn_intervals(eq,xseq)

The first six rows of the table display the results of the LT versus LS relationship. In this context, x1 represents the independent variable, while fit refers to the fitted values. Additionally, CI_L indicates the lower confidence interval, and CI_U indicates the upper confidence interval. Similarly, PI_L represents the lower predicted interval, and PI_U denotes the upper predicted interval.
x1	fit	CI_L	CI_U	PI_L	PI_U
8	6.450810	6.405704	6.495917	5.749724	7.151897
10	8.100567	8.060360	8.140774	7.399779	8.801355
12	9.750324	9.714849	9.785799	9.049791	10.450857
14	11.400081	11.369093	11.431069	10.699761	12.100401
16	13.049838	13.022970	13.076706	12.349688	13.749988
18	14.699595	14.676284	14.722906	13.999573	15.399617

ⓘ To enhance the visualization of the function results, tables and their headers were constructed using the knitr and kableExtra packages. The code is not displayed.

fn_fyield()

The function calculates the fillet yield by dividing a defined weight reference point bm by the mean, lower, and upper confidence interval of 95% (IC95%) of the estimated fillet weight, respectively. These values are obtained from the list items l_intervals$CI returned by the function Morefi::fn_intervals().

If the analyzed regression has fillet weight as an independent variable, then values are calculated. An “if statement” is written for this propose.

Fillet yield was calculated for a sequence of the independent variable (including minimum and maximum values). The function fn_fyield() returms a table with fillet yield results.

The function requires defining:

i An integer value that indicates which regression analysis to use.
bm An integer value used as a benchmark.
df A data frame with landed weights for each category.

Example

CI comes from fn_intervals() example

bm <- 18
df <- CI
i <- 1
yield1 <- fn_fyield(i,bm,df)
i <- 1
yield2 <- fn_fyield(i,bm,df)

The first six rows of the table are displayed, based on the LT versus LS relationship results. In this context, x1 represents the independent variable, while fit refers to the fitted values. Additionally, CI_L indicates the lower confidence interval, and CI_U indicates the upper confidence interval. Similarly, PI_L represents the lower predicted interval, and PI_U denotes the upper predicted interval.
x1	fit	CI_L	CI_U	PI_L	PI_U	Yfit	YIC_L	YIC_U	YIP_L	YIP_U
8	6.450810	6.405704	6.495917	5.749724	7.151897	2.7903471	2.8099957	2.7709715	3.1305851	2.5168149
10	8.100567	8.060360	8.140774	7.399779	8.801355	2.2220666	2.2331508	2.2110919	2.4325051	2.0451395
12	9.750324	9.714849	9.785799	9.049791	10.450857	1.8460925	1.8528338	1.8394001	1.9889961	1.7223468
14	11.400081	11.369093	11.431069	10.699761	12.100401	1.5789361	1.5832397	1.5746559	1.6822805	1.4875540
16	13.049838	13.022970	13.076706	12.349688	13.749988	1.3793275	1.3821732	1.3764934	1.4575266	1.3090921
18	14.699595	14.676284	14.722906	13.999573	15.399617	1.2245235	1.2264685	1.2225847	1.2857535	1.1688602
20	16.349352	16.328742	16.369962	15.649415	17.049289	1.1009611	1.1023507	1.0995749	1.1502028	1.0557625
22	17.999109	17.979977	18.018241	17.299214	18.699004	1.0000495	1.0011136	0.9989876	1.0405097	0.9626181
24	19.648866	19.629704	19.668028	18.948970	20.348762	0.9160834	0.9169777	0.9151909	0.9499197	0.8845747
26	21.298623	21.277930	21.319315	20.598683	21.998562	0.8451251	0.8459469	0.8443048	0.8738423	0.8182353

The first six rows of the table are displayed, based on the LT versus WT relationship results. In this context, x1 represents the independent variable, while fit refers to the fitted values. Additionally, CI_L indicates the lower confidence interval, and CI_U indicates the upper confidence interval. Similarly, PI_L represents the lower predicted interval, and PI_U denotes the upper predicted interval.
x1	fit	CI_L	CI_U	PI_L	PI_U	Yfit	YIC_L	YIC_U	YIP_L	YIP_U
8	6.450810	6.405704	6.495917	5.749724	7.151897	2.7903471	2.8099957	2.7709715	3.1305851	2.5168149
10	8.100567	8.060360	8.140774	7.399779	8.801355	2.2220666	2.2331508	2.2110919	2.4325051	2.0451395
12	9.750324	9.714849	9.785799	9.049791	10.450857	1.8460925	1.8528338	1.8394001	1.9889961	1.7223468
14	11.400081	11.369093	11.431069	10.699761	12.100401	1.5789361	1.5832397	1.5746559	1.6822805	1.4875540
16	13.049838	13.022970	13.076706	12.349688	13.749988	1.3793275	1.3821732	1.3764934	1.4575266	1.3090921
18	14.699595	14.676284	14.722906	13.999573	15.399617	1.2245235	1.2264685	1.2225847	1.2857535	1.1688602
20	16.349352	16.328742	16.369962	15.649415	17.049289	1.1009611	1.1023507	1.0995749	1.1502028	1.0557625
22	17.999109	17.979977	18.018241	17.299214	18.699004	1.0000495	1.0011136	0.9989876	1.0405097	0.9626181
24	19.648866	19.629704	19.668028	18.948970	20.348762	0.9160834	0.9169777	0.9151909	0.9499197	0.8845747
26	21.298623	21.277930	21.319315	20.598683	21.998562	0.8451251	0.8459469	0.8443048	0.8738423	0.8182353

ⓘ To enhance the visualization of the function results, tables and their headers were constructed using the knitr and kableExtra packages. The code is not displayed.

fn_R2RV()

The function calculates a robust version of the coefficient of determination $R^{2}_{RV}$ using the Equation Summary values fitted with the robustbase::nlrob() function.

This is the consistency corrected robust coefficient of determination by Renaud and Victoria-Feser (2010) which allows for a possible correction factor a for consistency considerations.

Inside the function:

The vectors of observed (y1), predicted (yc) and weighted (W) values are obtained from the summary model (eq).

The value of the Weighted Estimate Average (ywea), the modified sum of squares for explained (SSEw), total (SSTw), and residual (SSRw) were estimated.

The correction factor value for consistency considerations a for 95 percent was also obtained from summary model (eq).

A vector with the robust version of the coefficient of determination R2wa and its adjusted value R2wa_adj were returned as a vector.

In the function, the following were estimated:

The Weighted Estimate Average $\overline{\widehat{y}}_{w}$ (called as ywea).

$\overline{\widehat{y}}_{w}=\left(1/\Sigma w_{i}\right)\times \Sigma w_{i} \widehat{y}_{i}$

The modified sum of squares explained SSEw $SSEw= \sum_{}^{}w_{i}(\widehat{y}_{i}-\overline{\widehat{y}}_{w}) ^2)$

In this function, the robust residual standard error $(RSE_{R})$ was utilized, and the modified sum of squared residuals was computed $SSRw$ .

$SSRw= df* (RSE_{R})^2)$

The variables $(RSE_{R})$ and $df$ (degrees of freedom) were obtained from the model summary.

The robust version of the coefficient of determination $R^{2}_{w,a}$ $R^{2}_{w,a}=\frac{SSEw}{SSEw+a\times SSRw}$ The adjusted coefficient of determination $R^{2}_{adj,w,a}$ $R^{2}_{adj,w,a}=1- \left(1- R^{2}_{w,a}\right)\times \left( \frac{n-1 }{n-q} \right)$

where $y1_{i}$ , and $\widehat{y}_{i}$ are the $i_{th}$ observed and predicted values, $a$ is the correction factor value for consistency considerations for 95 percent, $n$ the number of pairs of observations and $q$ the number of variables included in the model.

The function requires defining:

eq Summary of the equation fitted using robustbase::nlrob() function.

The function returns the a vector with the robust version of the coefficient of determination $R^{2}_{w,a}$ and its adjusted value $R^{2}_{adj,w,a}$ .

Example

The objecteq2 originates from the example fn_dfa().

The function returns a vector containing both $R^{2}$ and the adjusted $R^{2}_{adj}$ values.

R2wa <- fn_R2RV(eq=eq2)
#> [1] 0.9805933 0.9805794

fn_summary()

The function creates a customized table that displays the regression summary categorized by model and landed weight types: Fresh, Frozen-thawed (Frozen), and Total. The 95% confidence interval is noted in parentheses. Additionally, the adjusted coefficient of determination (R2) and the degrees of freedom (DF) are also reported.

The function requires defining:

List_Tables A list to store summary regression results.
modelos A character vector containing the variables of a function.
catego A character vector containing the landed weight categories.
eq Summary of the equation fitted.
R2 A numeric value of the adjusted robust version of the coefficient of determination.
i An integer value indicating the ith regression analyzed.
j An integer value indicating the jth categorie analyzed.

Summary Regression Table.

To store the summary regression, a customised table T1 is generated. The type of function model (Linear or Potential), and its variables, are indicated in the first two columns. The third column indicates the data source used (Fresh, Fresh-Thawed, or Total). By row it is stored: the Intercept, its confidence interval (CI95%); the Slope; its (CI95%); the adjusted robust coefficient of determination R2,adj,w,a and the degrees of freedom DF.

    # An empty table to store the summary regression results   
catego <- c("Total") 
nr <- length(catego)

T1 <- data.frame(matrix(NA, nrow = nr, ncol = 9))
names(T1) <- c("Function", "Model","Categories",
               "Intercept", "CI95%","Slope",
               "CI95%", "R2","DF")
T1
#>   Function Model Categories Intercept CI95% Slope CI95% R2 DF
#> 1       NA    NA         NA        NA    NA    NA    NA NA NA

List_Tables store regression results

To store the results of each fitted model, a list called List_Tables was created. Each item in the list contains the customized table T1, which is initially filled with NA values.


# Create model list including empty T1 table
List_Tables <- setNames(lapply(1:length(modelos), function(x)
T1),names(modelos))

Example

Aqui

# Performing the table

#T_sum <- dplyr::bind_rows(List_Tables)

# Changing Model labels for the Table
# Insert three NA between values of vector row_name
#mdls <- as.vector(t(cbind(row_name, matrix(NA, nrow = length(row_name), ncol = 2))))
#T_sum$Model <- mdls


modelos <- modelos
catego <- c("Total")
j <- 1
i <- 1

# Linnear equation
eq <- eq1
# R squared
R2 <- summary(eq)$r.squared 
#Non parametric IC 95 for parameters
#betas_IC95 <- confint(eq, level = 0.95)

List_Tables[[i]][j,] <- fn_summary(List_Tables, modelos, catego, eq, R2, i, j)
#>   Function        Model Categories  Intercept            CI95%     Slope
#> 1   Linear LT vs. vs.LS      Total -0.1482175 (-0.21 to -0.08) 0.8248785
#>            CI95%       R2   DF
#> 1 (0.82 to 0.83) 0.996128 1395
i <- 2

# Non nonlinear regression (Potential)  
eq <- eq2
# R2 bobust version
R2 <- Morefi::fn_R2RV(eq)[2]
#> [1] 0.9805933 0.9805794
#IC 95 Non parametric for parameters
betas_IC95 <- confint(eq,method = "Wald")  
List_Tables[[i]][j,] <- fn_summary(List_Tables, modelos, catego, eq, R2, i, j)
#>   Function        Model Categories  Intercept          CI95%    Slope
#> 1   Linear LT vs. vs.WT      Total 0.01747118 (0.02 to 0.02) 3.085355
#>            CI95%        R2   DF
#> 1 (3.06 to 3.11) 0.9805794 1395

Regression summarized by model and landed weight categories: Fresh, Frozen-thawed (Frozen) and Total, for the bullseye puffer <i>Sphoeroides annulatus</i>. The 95% confidence interval parameter is in parentheses. Adjusted robust coefficient of determination ( $R^{2}_{adj}$ ) and Degrees of Freedom (DF) are also reported. Acronyms used: Total length ( $L_{T}$ ) standard length ( $L_{S}$ ) body trunk length ( $L_{B}$ ) total weight ( $W_{T}$ ) body trunk weight ( $W_{B}$ ) and fillet weight ( $W_{fi}$ ).
Function	Model	Categories	Intercept	CI95%	Slope	CI95%	R2	DF
Linear	LT vs. vs.LS	Total	-0.1482175	(-0.21 to -0.08)	0.8248785	(0.82 to 0.83)	0.996128	1395

ⓘ To enhance the visualization of the function results, tables and their headers were constructed using the knitr and kableExtra packages. The code is not displayed.

Aqui

fn_Wlive()

fn_Wlive(): The live weight, which is the total weight of an organism, is estimated based on the weights of different landing categories, such as eviscerated weight and fillet weight. These estimates are derived using regression parameters that relate total weight to the weight of each landing category.

Example

catch cames from Data available in the package/data Bullseye puffer fish landings explanation.


#List_Tables <- 
#mfi <- 
#List_TCCT <-  

Biomass <- catch
#Table1 <- fn_Wlive(List_Tables, mfi, List_TCCT, Biomass)

Plot functions

To assist with analysis, three functions have been created to generate a composite figure: fn_fig_e(), fn_fig_fw(), and fn_fig_w(). The data points in these figures are color-coded according to a weighted scale, and the titles of each graph include subscripts. Each of these functions has identical attributes, which are described below:

df A data frame contains the following variables: independent (x) and dependent (y) variables, the fitted variable (fitt), a weighted variable (wi), and additional details including the weights (wi), fitted values (fitt), residuals (ei), and the scale.

The df is derived from the results of the fn_dfa() function described earlier.

# Preparing the dataset.
library(dplyr)
tmp1 <- dfa1              # Data frame 1
tmp1['id'] = "LT_LS"      # to add an ID column to a Data frame

tmp2 <- dfa2              # Data frame 2
tmp2['id'] = "LT_WT"      # to add an ID column to a Data Frame

df <- rbind(tmp1, tmp2)   # Joining data sets

opacity A numeric value for the alpha aesthetic used to control the transparency of elements in a plot.

opacity <- 0.7

tint A vector that specifies the palette colors used to color the points.

tint <- c("#000000", "#009E73", "#56B4E9")

scale A numeric vector that defines the thresholds for coloring the points.

The observed data points were coloured based on a weighted scale $(w_{i})$ : blue for unweighted $(w_{i}=1)$ , green for weighted $(1>w_{i}≥0.25)$ , and black for outliers $(w_{i}<0.25)$ . Lengths in cm and weights in g.

# weighted value scale
wi_scale <- c(0.000, 0.249, 0.990, 1.000)

order A vector determines the sequence of the plots.

# To order facet wrap plots in ggplot2
X_names <- c("LT_LS", "LT_WT")

my_labeller Transforms objects to labeller functions. Used internally by labeller().

Since the parameters contain subscripts, the labels were customized using the ggplot2::as_labeller() function and are stored in my_labeller.

# The labels in the ggplot composite chart are customized to include subscripts.
library(ggplot2)
my_labeller <- as_labeller(c(LT_LS=  "L[T]-L[S]",
                             LT_WT=  "L[T]-W[T]"),
                           default = label_parsed)

fn_fig_e()

The function creates a graph that displays residuals on the vertical axis and either the independent variable or predicted values on the horizontal axis, as determined by the researcher.

Example

A residual analysis of the model fitting has been conducted using combined data sets for the pufferfish Sphoeroides annulatus. The label in the grey box indicates the variables used for each model; the first variable listed is the independent variable, and the second is the dependent variable. The x-axis represents the values of the independent variable, while the y-axis displays the raw residuals (ei).

The standard graphical output, along with the one customized using the theme papers() function, is displayed.

# standard graphical output
p <- fn_fig_e(df, opacity, tint, scale= wi_scale,
              order= X_names, my_labeller)

# theme papers()
p + theme_papers

fn_fig_fw()

The fitted values of the models for a landed presentation category were displayed as a multi-panel plot. The observed data points for each fitted relationship were categorized according to a weighted color scale.

Example

Using the biometric data from Morefi::botete, a linear relationship between Total Length and Standard Length (LT_LS) was established using the robustbase::lmrob function. Additionally, the relationship between Total Length and Total Weight (LT_WT) was fitted using the robustbase::nlm function, with an input y-value of a = 0.1 and a slope of b = 3.

The label in the grey box indicates the variables used for each model; the first variable listed is the independent variable, and the second is the dependent variable. The x-axis represents the values of the independent variable, while the y-axis displays the raw residuals (ei).

The standard graphical output, along with the one customized using the theme papers() function, is displayed.

# standard graphical output
p <- fn_fig_fw(df, opacity, tint, scale= wi_scale,
               order= X_names, my_labeller)

# theme papers()
p + theme_papers

fn_fig_w()

The residual structure was analyzed by graphing residuals against weighted values. A custom multi-panel plot illustrates the structure of each fitted relationship, categorized by a color-weighted scale of values.

Example

The Residual Structures classified by a Weighted Scale was analyzed using combined data sets for the pufferfish Sphoeroides annulatus. The label in the grey box indicates the variables used for each model; the raw residuals are shown on the x-axis, and the weighted residuals (wi) are displayed on the y-axis.

The x-axis label is defined in the lab_x object, while the y-axis label is defined in the lab_y object. In this example, both labels are italicized, with the i-th label formatted as a subscript.

The standard graphical output, along with the one customized using the theme papers() function, is displayed.

# standard graphical output
lab_x <- expression(italic(e[i]))
lab_y <- expression(italic(w[i]))

# Plot of Residual Structures Classified by a Weighted Scale.
p <- fn_fig_w(df, opacity,tint, my_labeller,order= X_names, lab_x, lab_y)

 
# theme papers()
p + theme_papers

References

Aguirre-Villaseñor, H., Morales-Bojórquez, E., & Cisneros-Mata, M. Á. (2025). Biometric relationships as a fisheries management tool: A case study on the bullseye puffer (Sphoeroides annulatus) in an artisanal fishery. Fisheries Research, 292, 107593. DOI

Chen, Y., Jackson, D. A., Harvey, H. H. 1992. A comparison of von Bertalanffy and polynomial functions in modelling fish growth data. Canadian Journal of Fisheries and Aquatic Sciences 49(6): 1228–1235. DOI

Maechler M, Rousseeuw P, Croux C, Todorov V, Ruckstuhl A, Salibian-Barrera M, Verbeke T, Koller M, Conceicao EL, Anna di Palma M (2024). robustbase: Basic Robust Statistics. R package version 0.99-4-1, DOI

Renaud, O., Victoria-Feser, M. P. (2010). A robust coefficient of determination for regression. Journal of Statistical Planning and Inference. 140(7), 1852-1862. DOI

SIPESCA. 2024. Sistema de Información de Pesca y Acuacultura – SIPESCA. Comisión Nacional de Pesca y Acuacultura. SIPESCA

Citation

Aguirre-Villaseñor H (2024). Morefi: Morphological Relationships Fitted by Robust Regression. R package version 0.1.0, https://macrurido.github.io/Morefi/.

@Manual{,
  title = {Morefi: Morphological Relationships Fitted by Robust Regression},
  author = {Hugo Aguirre-Villaseñor},
  year = {2024},
  note = {R package version 0.1.0},
  url = {https://macrurido.github.io/Morefi/},
}

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Morefi

03 October 2026

Morefi: Example Analysis

Installation

Data available in the package

Bullseye puffer measures

Bullseye puffer fish landings

theme_papers()

Values to define for the examples

List: modelos

Morefi functions

Analysis functions

fn_ARSS()

Example

fn_dfa()

Example

fn_freq()

fn_freqw()

Example

fn_xseq()

Example

fn_intervals()

Example

fn_fyield()

Example

fn_R2RV()

Example

fn_summary()

Summary Regression Table.

List_Tables store regression results

Example

Aqui

Aqui

fn_Wlive()

Example

Plot functions

fn_fig_e()

Example

fn_fig_fw()

Example

fn_fig_w()

Example

References

Citation