1 Leitura e preparo

#-----------------------------------------------------------------------
#                                            Prof. Dr. Walmes M. Zeviani
#                                leg.ufpr.br/~walmes · github.com/walmes
#                                        walmes@ufpr.br · @walmeszeviani
#                      Laboratory of Statistics and Geoinformation (LEG)
#                Department of Statistics · Federal University of Paraná
#                                       2020-set-25 · Curitiba/PR/Brazil
#-----------------------------------------------------------------------

#-----------------------------------------------------------------------
# Pacotes.

rm(list = objects())

library(lattice)
library(latticeExtra)
library(tidyverse)

my_palette <- colorRampPalette(
    RColorBrewer::brewer.pal(n = 11, name = "Spectral"),
    space = "rgb")

#-----------------------------------------------------------------------
# Importação.

# ATTENTION: tabela extraída de
# `Luciane Rozwalka.zip` > /Luciane Rozwalka/pessego/latencia.xls
tb <- read_tsv("chimarrita-maciel.txt",
               locale = locale(decimal_mark = ","),
               na = c("", "?"))
attr(tb, "spec") <- NULL
str(tb)
## spc_tbl_ [448 × 24] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
##  $ cultivar : chr [1:448] "maciel" "maciel" "maciel" "maciel" ...
##  $ ferimento: chr [1:448] "sim" "sim" "sim" "sim" ...
##  $ lado     : chr [1:448] "inoculado" "inoculado" "inoculado" "inoculado" ...
##  $ fruto    : num [1:448] 1 2 3 4 5 6 7 8 9 10 ...
##  $ cor0     : num [1:448] 91.1 92.1 110.1 103.2 100.9 ...
##  $ ida0     : num [1:448] 1.45 1.09 2.08 1.18 1.75 0.33 1.26 1.36 2.08 1.64 ...
##  $ ida48    : num [1:448] 1.19 0.68 2.17 NA 1.55 0.33 0.97 1.15 2.12 1.47 ...
##  $ ida60    : num [1:448] 1.24 0.66 2.1 1.81 1.53 0.53 1.17 1.19 2.13 1.44 ...
##  $ ms0      : num [1:448] 20.4 18.9 10.9 11.2 18 ...
##  $ ms48     : num [1:448] 16.9 18.3 10.1 12 18.4 ...
##  $ ms60     : num [1:448] 17.7 18.4 11.3 14.2 17.6 ...
##  $ ss0      : num [1:448] 10.86 10.95 6.94 11.69 11.75 ...
##  $ ss48     : num [1:448] 12.99 12.58 8.52 14.86 13.79 ...
##  $ ss60     : num [1:448] 8.72 9.55 3.92 8.35 10.01 ...
##  $ f0       : num [1:448] 5.79 4.46 8.79 7.2 7.44 3.19 4.67 5.76 7.7 6.28 ...
##  $ f48      : num [1:448] 3.68 2.94 7.71 6.17 4.87 3.8 2.77 4.22 6.83 4.62 ...
##  $ f60      : num [1:448] 4.72 3.21 8.22 7.47 5.92 4.77 5.58 6.56 7.59 6.8 ...
##  $ b0       : num [1:448] 12.5 12.9 10.5 10.5 12.9 ...
##  $ b48      : num [1:448] 11.74 12.45 9.86 10.32 11.75 ...
##  $ b60      : num [1:448] 11.69 13.27 9.82 10.41 12.02 ...
##  $ le48     : num [1:448] 5.42 2.03 5.11 NA 5.81 ...
##  $ le60     : num [1:448] 19.5 14.2 21.5 20.2 23.7 ...
##  $ la48     : num [1:448] 0 0 0 0 0 1 0 0 0 0 ...
##  $ la60     : num [1:448] 0 0 0 0 0 1 0 0 0 1 ...
##  - attr(*, "problems")=<externalptr>
# Inspeção.
ftable(xtabs(~cultivar + ferimento + lado, data = tb))
##                      lado inoculado não inoculado
## cultivar   ferimento                             
## chimarrita não                   56            56
##            sim                   56            56
## maciel     não                   56            56
##            sim                   56            56
# Dentro do fruto tem os lados inoculado e não inoculado.
tb %>%
    filter(cultivar == "maciel",
           ferimento == "sim",
           fruto %in% 1:10) %>%
    arrange(fruto, lado)
## # A tibble: 20 × 24
##    culti…¹ ferim…² lado  fruto  cor0  ida0 ida48 ida60   ms0  ms48  ms60
##    <chr>   <chr>   <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
##  1 maciel  sim     inoc…     1  91.1  1.45  1.19  1.24  20.4  17.0  17.7
##  2 maciel  sim     não …     1  98.2  1.29  1.1   0.9   17.4  17.7  15.7
##  3 maciel  sim     inoc…     2  92.1  1.09  0.68  0.66  18.9  18.3  18.4
##  4 maciel  sim     não …     2  92.6  0.97  0.76  0.66  19.9  19.0  18.0
##  5 maciel  sim     inoc…     3 110.   2.08  2.17  2.1   10.9  10.1  11.3
##  6 maciel  sim     não …     3 109.   2.17  2.13  2.07   9    10.7  10.5
##  7 maciel  sim     inoc…     4 103.   1.18 NA     1.81  11.2  12    14.2
##  8 maciel  sim     não …     4 107.   1.64 NA     1.86  12.6  14.2  13.4
##  9 maciel  sim     inoc…     5 101.   1.75  1.55  1.53  18    18.4  17.6
## 10 maciel  sim     não …     5  92.2  1.55  0.82  0.78  18.4  18.1  17.7
## 11 maciel  sim     inoc…     6  84.6  0.33  0.33  0.53  20.6  21.5  23.9
## 12 maciel  sim     não …     6  77.6  0.17  0.12  0.08  21.7  20.7  19.5
## 13 maciel  sim     inoc…     7  94.0  1.26  0.97  1.17  16.4  17.0  18.0
## 14 maciel  sim     não …     7 175.   1.41  1.03  0.98  17.9  17.5  16.5
## 15 maciel  sim     inoc…     8  94.0  1.36  1.15  1.19  17.5  18.2  18.0
## 16 maciel  sim     não …     8 105.   1.41  1.8   1.67  12.1  12.4  13.1
## 17 maciel  sim     inoc…     9 109.   2.08  2.12  2.13  14.5  13.6  10.2
## 18 maciel  sim     não …     9 107.   2.12  2.06  2.04  13.0  13.8  11.1
## 19 maciel  sim     inoc…    10 100.   1.64  1.47  1.44  11.2  14.8  16.8
## 20 maciel  sim     não …    10 103.   1.8   1.81  1.66  12.4  14.3  12.2
## # … with 13 more variables: ss0 <dbl>, ss48 <dbl>, ss60 <dbl>,
## #   f0 <dbl>, f48 <dbl>, f60 <dbl>, b0 <dbl>, b48 <dbl>, b60 <dbl>,
## #   le48 <dbl>, le60 <dbl>, la48 <dbl>, la60 <dbl>, and abbreviated
## #   variable names ¹​cultivar, ²​ferimento
#-----------------------------------------------------------------------
# Recodificação.

tb <- tb %>%
    mutate(ferimento = recode(ferimento,
                              "sim" = "W",
                              "não" = "noW"),
           cultivar = recode(cultivar,
                             "chimarrita" = "Chimarrita",
                             "maciel" = "Maciel"),
           lado = recode(lado,
                         "inoculado" = "Is",
                         "não inoculado" = "OsIs"))


tb %>%
    count(cultivar, lado)
## # A tibble: 4 × 3
##   cultivar   lado      n
##   <chr>      <chr> <int>
## 1 Chimarrita Is      112
## 2 Chimarrita OsIs    112
## 3 Maciel     Is      112
## 4 Maciel     OsIs    112

2 Análise exploratória

2.1 Análise gráfica

#-----------------------------------------------------------------------
# Análise gráfica.

# Empilha as variáveis.
tb_l <- tb %>%
    pivot_longer(cols = -(cultivar:fruto),
                 names_to = "variable",
                 values_to = "value") %>%
    # gather(key = "variable", value = "value", -(cultivar:fruto)) %>%
    mutate(trat = sprintf("%s-%s:%s",
                          lado, ferimento, str_remove(variable, "\\D+")),
           mea = str_remove(variable, "\\d+"),
           tempo = as.integer(str_remove(variable, "\\D+")))
str(tb_l)
## tibble [8,960 × 9] (S3: tbl_df/tbl/data.frame)
##  $ cultivar : chr [1:8960] "Maciel" "Maciel" "Maciel" "Maciel" ...
##  $ ferimento: chr [1:8960] "W" "W" "W" "W" ...
##  $ lado     : chr [1:8960] "Is" "Is" "Is" "Is" ...
##  $ fruto    : num [1:8960] 1 1 1 1 1 1 1 1 1 1 ...
##  $ variable : chr [1:8960] "cor0" "ida0" "ida48" "ida60" ...
##  $ value    : num [1:8960] 91.09 1.45 1.19 1.24 20.4 ...
##  $ trat     : chr [1:8960] "Is-W:0" "Is-W:0" "Is-W:48" "Is-W:60" ...
##  $ mea      : chr [1:8960] "cor" "ida" "ida" "ida" ...
##  $ tempo    : int [1:8960] 0 0 48 60 0 48 60 0 48 60 ...
# unique(tb_l$mea)

# Para recodificação.
v <- list(ida = "DA index",
          ms = "Dry matter",
          ss = "Titratable acidity",
          f = "Firmness (N)",
          b = "°Brix")

# Faz a recodificação.
tb_l <- tb_l %>%
    mutate(mea = recode(mea, !!!v))

# unique(tb_l$mea)

# Compara os lados do fruto.
tb_side <- tb_l %>%
    mutate(id = paste0(cultivar, fruto)) %>%
    select(-trat) %>%
    # spread(key = lado, value = value) %>%
    pivot_wider(names_from = "lado", values_from = "value") %>%
    mutate(d = Is - OsIs)
cap <- "Physicochemical characteristics (median, 25 and 75th percentile, minimum and maximum values excluding outliers and outliers) measured on inoculated side without wound (Is-noW), opposite side not inoculated of fruit without wound (OsIs-noW), inoculated side with wound (Is-W) and opposite side not inoculated of inoculated fruit with wound (OsIs-W) of ‘Chimarrita’ and ‘Maciel’ cultivars in postharvest using non-destructive methodology, in the moment of inoculation (time 0) and 48 and 60 h post inoculation. Pelotas, RS. Solid lines indicate mean trend for each combination of fruit side and wound."

# Apresenta os dados.
ggplot(data = filter(tb_l, is.element(mea, unlist(v))),
       mapping = aes(x = trat, y = value)) +
    facet_grid(facets = mea ~ cultivar,
               scales = "free") +
    geom_boxplot() +
    stat_summary(mapping = aes(group = paste(lado, ferimento)),
                 geom = "line",
                 fun = "mean",
                 color = "red") +
    labs(y = "Physicochemical characteristics\n(value)",
         x = "Treatment:Time after inoculation (h)") +
    theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))
Physicochemical characteristics (median, 25 and 75th percentile, minimum and maximum values excluding outliers and outliers) measured on inoculated side without wound (Is-noW), opposite side not inoculated of fruit without wound (OsIs-noW), inoculated side with wound (Is-W) and opposite side not inoculated of inoculated fruit with wound (OsIs-W) of ‘Chimarrita’ and ‘Maciel’ cultivars in postharvest using non-destructive methodology, in the moment of inoculation (time 0) and 48 and 60 h post inoculation. Pelotas, RS. Solid lines indicate mean trend for each combination of fruit side and wound.

Physicochemical characteristics (median, 25 and 75th percentile, minimum and maximum values excluding outliers and outliers) measured on inoculated side without wound (Is-noW), opposite side not inoculated of fruit without wound (OsIs-noW), inoculated side with wound (Is-W) and opposite side not inoculated of inoculated fruit with wound (OsIs-W) of ‘Chimarrita’ and ‘Maciel’ cultivars in postharvest using non-destructive methodology, in the moment of inoculation (time 0) and 48 and 60 h post inoculation. Pelotas, RS. Solid lines indicate mean trend for each combination of fruit side and wound.

O gráfico mostra que o efeito do tempo na média das variáveis é maior para a cultivar Chimarrita. Alterações nas variáveis são maiores para o lado do fruto inoculado e com ferimento.

cap <- "Difference in physicochemical properties (median, 25 and 75th percentile, minimum and maximum values excluding outliers and outliers) measured on the inoculated side with wound (Is-W) and opposite side not inoculated of inoculated fruit with wound (OsIs-W), of ‘Chimarrita’ and ‘Maciel’ cultivars in postharvest using non-destructive methodology, in the moment of inoculation (time 0) and 48 and 60 h post inoculation. Pelotas, RS, Brazil. Solid lines indicate mean trend."

# Visualiza as diferenças.
ggplot(data = filter(tb_side, is.element(mea, unlist(v))),
       mapping = aes(x = paste(ferimento, tempo, sep = ":"),
                     y = d)) +
    facet_grid(facets = mea ~ cultivar, scales = "free") +
    geom_boxplot() +
    stat_summary(mapping = aes(group = ferimento),
                 geom = "line",
                 fun = "mean",
                 color = "red") +
    labs(y = "Physicochemical characteristics\n(difference between sides)",
         x = "Wound:Time after inoculation (h)") +
    theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))
Difference in physicochemical properties (median, 25 and 75th percentile, minimum and maximum values excluding outliers and outliers) measured on the inoculated side with wound (Is-W) and opposite side not inoculated of inoculated fruit with wound (OsIs-W), of ‘Chimarrita’ and ‘Maciel’ cultivars in postharvest using non-destructive methodology, in the moment of inoculation (time 0) and 48 and 60 h post inoculation. Pelotas, RS, Brazil. Solid lines indicate mean trend.

Difference in physicochemical properties (median, 25 and 75th percentile, minimum and maximum values excluding outliers and outliers) measured on the inoculated side with wound (Is-W) and opposite side not inoculated of inoculated fruit with wound (OsIs-W), of ‘Chimarrita’ and ‘Maciel’ cultivars in postharvest using non-destructive methodology, in the moment of inoculation (time 0) and 48 and 60 h post inoculation. Pelotas, RS, Brazil. Solid lines indicate mean trend.

O gráfico mostra a diferença no valor das variáveis comparando os lados do fruto. Para os frutos sem ferimento, verifica-se não haver diferença nas variáveis comparando-se os lados. Por outro lado, para frutos com ferimento, observa-se diferença nas variáveis entre os lados. Nos frutos de chimarrita a alteração ocorre para todas as variáveis, exceto DA index. Para frutos de maciel, observa-se alteração apenas nas variáveis firmness e total soluble acidity.

cap <- "Physicochemical properties measured on wounded and no wounded fruits for combinations among cultivars, fruit side and time. Two sample t-test is used to test the effect wound (codification for the p-values: `*** < 0.001`, `** < 0.01`, `* < 0.05`, `. < 0.1` and `ns >= 0.1`). Pelotas, RS, Brazil."

# Teste t para comparar com vs sem ferimento.
u <- unique(tb_l$variable) |> head(n = -4)
tb_ttest <- tb_l %>%
    filter(variable %in% u) %>%
    mutate(lado_tempo = paste(lado, tempo, sep = ":")) %>%
    group_by(cultivar, lado_tempo, variable) %>%
    do({
        tb_ttest <- . |>
            rstatix::t_test(value ~ ferimento,
                            var.equal = TRUE,
                            detailed = TRUE,
                            p.adjust.method = "none")
        tb_max <- . |>
            summarise(max_value = extendrange(value, f = 0.1)[2])
        bind_cols(tb_ttest, tb_max)
    }) %>%
    ungroup() %>%
    left_join(distinct(tb_l, variable, mea))
## Joining with `by = join_by(variable)`
# str(tb_ttest)

tb_ttest <- tb_ttest %>%
    mutate(p_signif = cut(p,
                          breaks = c(0, 0.001, 0.01, 0.05, 0.1, 1),
                          labels = c("***", "**", "*", ".", "ns")))

tb_l %>%
    filter(mea %in% v) %>%
    # filter(variable %in% u) %>%
    mutate(lado_tempo = paste(lado, tempo, sep = ":")) %>%
    ggpubr::ggboxplot(
        x = "ferimento",
        y = "value",
        # x = "lado_tempo",
        ggtheme = theme_gray()
    ) +
    facet_grid(mea ~ cultivar + lado_tempo, scale = "free") +
    ggpubr::stat_pvalue_manual(
        filter(tb_ttest, mea %in% v),
        # label = "p = {sprintf('%0.4f', p)}",
        label = "p_signif",
        y.position = "max_value") +
    labs(y = "Physicochemical characteristics\n(value)",
         x = "Treatment") +
    theme(axis.text.x = element_text(angle = 90, hjust = 1, vjust = 0.5))
Physicochemical properties measured on wounded and no wounded fruits for combinations among cultivars, fruit side and time. Two sample t-test is used to test the effect wound (codification for the p-values: `*** < 0.001`, `** < 0.01`, `* < 0.05`, `. < 0.1` and `ns >= 0.1`). Pelotas, RS, Brazil.

Physicochemical properties measured on wounded and no wounded fruits for combinations among cultivars, fruit side and time. Two sample t-test is used to test the effect wound (codification for the p-values: *** < 0.001, ** < 0.01, * < 0.05, . < 0.1 and ns >= 0.1). Pelotas, RS, Brazil. 

cap <- "Results from t-tests. Pelotas, RS, Brazil."

# Exibe.
tb_ttest |>
    select(-c(".y.", "statistic", "df", "method",
              "alternative", "max_value", "group1", "group2")) |>
    relocate(c("cultivar", "mea", "variable", "lado_tempo",
               "estimate1", "estimate2", "estimate")) |>
    rename("noW_average" = "estimate1",
           "W_average" = "estimate2",
           "difference" = "estimate") |>
    knitr::kable(caption = cap)
Results from t-tests. Pelotas, RS, Brazil.
cultivar mea variable lado_tempo noW_average W_average difference n1 n2 p conf.low conf.high p_signif
Chimarrita °Brix b0 Is:0 12.0153571 12.2223214 -0.2069643 56 56 3.16e-01 -0.6144274 0.2004989 ns
Chimarrita cor cor0 Is:0 84.8576786 76.8185714 8.0391071 56 56 9.39e-02 -1.3877303 17.4659446 .
Chimarrita Firmness (N) f0 Is:0 5.7587500 5.6476786 0.1110714 56 56 4.33e-01 -0.1685603 0.3907032 ns
Chimarrita DA index ida0 Is:0 1.5003571 1.5264286 -0.0260714 56 56 6.73e-01 -0.1480501 0.0959073 ns
Chimarrita Dry matter ms0 Is:0 9.7900000 11.6840000 -1.8940000 51 45 2.34e-02 -3.5259719 -0.2620281 *
Chimarrita Titratable acidity ss0 Is:0 7.1051786 7.2371429 -0.1319643 56 56 5.96e-01 -0.6238869 0.3599583 ns
Chimarrita °Brix b48 Is:48 12.0332143 13.0457143 -1.0125000 56 56 4.30e-06 -1.4274021 -0.5975979 ***
Chimarrita Firmness (N) f48 Is:48 4.4303571 4.4616071 -0.0312500 56 56 9.00e-01 -0.5217227 0.4592227 ns
Chimarrita DA index ida48 Is:48 1.1617857 1.0310714 0.1307143 56 56 1.72e-01 -0.0575241 0.3189527 ns
Chimarrita Dry matter ms48 Is:48 14.0969231 8.9516327 5.1452904 52 49 0.00e+00 3.9272296 6.3633512 ***
Chimarrita Titratable acidity ss48 Is:48 7.0810714 4.2567857 2.8242857 56 56 0.00e+00 2.1848025 3.4637689 ***
Chimarrita °Brix b60 Is:60 12.2950909 14.0380357 -1.7429448 55 56 0.00e+00 -2.1879182 -1.2979714 ***
Chimarrita Firmness (N) f60 Is:60 3.7990909 5.3201786 -1.5210877 55 56 3.34e-04 -2.3347544 -0.7074209 ***
Chimarrita DA index ida60 Is:60 0.9883929 0.8001786 0.1882143 56 56 4.37e-02 0.0053920 0.3710365 *
Chimarrita Dry matter ms60 Is:60 14.3961538 5.5918605 8.8042934 52 43 0.00e+00 7.4481254 10.1604614 ***
Chimarrita Titratable acidity ss60 Is:60 5.8698182 -0.7089286 6.5787468 55 56 0.00e+00 5.5870348 7.5704587 ***
Chimarrita °Brix b0 OsIs:0 12.0939286 12.1491071 -0.0551786 56 56 7.90e-01 -0.4643864 0.3540293 ns
Chimarrita cor cor0 OsIs:0 68.6082143 78.1185714 -9.5103571 56 56 1.02e-01 -20.9517953 1.9310810 ns
Chimarrita Firmness (N) f0 OsIs:0 5.8814286 5.5860714 0.2953571 56 56 6.63e-02 -0.0201822 0.6108965 .
Chimarrita DA index ida0 OsIs:0 1.4953571 1.4592857 0.0360714 56 56 5.65e-01 -0.0879263 0.1600692 ns
Chimarrita Dry matter ms0 OsIs:0 9.6528000 10.7947826 -1.1419826 50 46 1.47e-01 -2.6910400 0.4070748 ns
Chimarrita Titratable acidity ss0 OsIs:0 7.1523214 7.2651786 -0.1128571 56 56 6.91e-01 -0.6743128 0.4485986 ns
Chimarrita °Brix b48 OsIs:48 11.7946429 11.9261818 -0.1315390 56 55 4.79e-01 -0.4981739 0.2350960 ns
Chimarrita Firmness (N) f48 OsIs:48 4.2205357 4.0905455 0.1299903 56 55 5.78e-01 -0.3312406 0.5912211 ns
Chimarrita DA index ida48 OsIs:48 1.0833929 1.0589286 0.0244643 56 56 8.00e-01 -0.1662120 0.2151406 ns
Chimarrita Dry matter ms48 OsIs:48 12.8978846 12.4891667 0.4087179 52 48 4.53e-01 -0.6676814 1.4851173 ns
Chimarrita Titratable acidity ss48 OsIs:48 6.9148214 6.8434545 0.0713669 56 55 8.26e-01 -0.5686643 0.7113980 ns
Chimarrita °Brix b60 OsIs:60 11.8705357 12.1116071 -0.2410714 56 56 2.36e-01 -0.6420101 0.1598673 ns
Chimarrita Firmness (N) f60 OsIs:60 3.4601786 3.2469643 0.2132143 56 56 4.34e-01 -0.3251204 0.7515490 ns
Chimarrita DA index ida60 OsIs:60 0.8732143 0.8360714 0.0371429 56 56 7.02e-01 -0.1547506 0.2290363 ns
Chimarrita Dry matter ms60 OsIs:60 13.4521154 11.8605882 1.5915271 52 51 1.29e-02 0.3439309 2.8391234 *
Chimarrita Titratable acidity ss60 OsIs:60 6.0019643 5.4566071 0.5453571 56 56 1.47e-01 -0.1939043 1.2846186 ns
Maciel °Brix b0 Is:0 11.5394643 11.6812500 -0.1417857 56 56 5.41e-01 -0.5996863 0.3161149 ns
Maciel cor cor0 Is:0 97.6207143 102.0453571 -4.4246429 56 56 1.88e-01 -11.0452845 2.1959988 ns
Maciel Firmness (N) f0 Is:0 5.6076786 6.0569643 -0.4492857 56 56 1.37e-01 -1.0436703 0.1450988 ns
Maciel DA index ida0 Is:0 1.4944643 1.5439286 -0.0494643 56 56 5.63e-01 -0.2185050 0.1195764 ns
Maciel Dry matter ms0 Is:0 15.4103571 15.1539286 0.2564286 56 56 6.62e-01 -0.9023286 1.4151857 ns
Maciel Titratable acidity ss0 Is:0 11.9983929 11.2857143 0.7126786 56 56 2.43e-02 0.0943954 1.3309617 *
Maciel °Brix b48 Is:48 11.5564286 11.3334545 0.2229740 56 55 3.38e-01 -0.2365768 0.6825249 ns
Maciel Firmness (N) f48 Is:48 5.4596429 4.5625000 0.8971429 56 56 1.02e-02 0.2167459 1.5775398 *
Maciel DA index ida48 Is:48 1.3451786 1.3900000 -0.0448214 56 55 6.72e-01 -0.2541540 0.1645111 ns
Maciel Dry matter ms48 Is:48 18.0621429 16.0046429 2.0575000 56 56 1.29e-03 0.8233530 3.2916470 **
Maciel Titratable acidity ss48 Is:48 12.1539286 12.8850000 -0.7310714 56 56 5.03e-02 -1.4631762 0.0010334 .
Maciel °Brix b60 Is:60 11.6544643 12.0346429 -0.3801786 56 56 1.08e-01 -0.8450329 0.0846757 ns
Maciel Firmness (N) f60 Is:60 3.8860714 5.9532143 -2.0671429 56 56 1.00e-07 -2.7790645 -1.3552212 ***
Maciel DA index ida60 Is:60 1.2400000 1.3328571 -0.0928571 56 56 3.58e-01 -0.2922401 0.1065258 ns
Maciel Dry matter ms60 Is:60 15.3675000 16.2160714 -0.8485714 56 56 1.69e-01 -2.0632800 0.3661371 ns
Maciel Titratable acidity ss60 Is:60 14.6882143 7.8021429 6.8860714 56 56 0.00e+00 5.6835835 8.0885594 ***
Maciel °Brix b0 OsIs:0 11.6016071 11.4494643 0.1521429 56 56 5.45e-01 -0.3441037 0.6483894 ns
Maciel cor cor0 OsIs:0 100.2151786 102.5873214 -2.3721429 56 56 6.09e-01 -11.5347603 6.7904746 ns
Maciel Firmness (N) f0 OsIs:0 5.6291071 5.8641071 -0.2350000 56 56 4.40e-01 -0.8362033 0.3662033 ns
Maciel DA index ida0 OsIs:0 1.4783929 1.4626786 0.0157143 56 56 8.68e-01 -0.1712112 0.2026397 ns
Maciel Dry matter ms0 OsIs:0 15.3221429 14.9132143 0.4089286 56 56 5.09e-01 -0.8153499 1.6332071 ns
Maciel Titratable acidity ss0 OsIs:0 12.0133929 11.5296429 0.4837500 56 56 1.26e-01 -0.1379925 1.1054925 ns
Maciel °Brix b48 OsIs:48 11.1478571 10.6908929 0.4569643 56 56 7.46e-02 -0.0460832 0.9600118 .
Maciel Firmness (N) f48 OsIs:48 5.3042857 4.1794643 1.1248214 56 56 1.21e-03 0.4541479 1.7954949 **
Maciel DA index ida48 OsIs:48 1.3228571 1.3370909 -0.0142338 56 55 8.94e-01 -0.2259688 0.1975013 ns
Maciel Dry matter ms48 OsIs:48 17.7314286 15.5273214 2.2041071 56 56 2.16e-04 1.0627140 3.3455003 ***
Maciel Titratable acidity ss48 OsIs:48 11.5387500 13.4658929 -1.9271429 56 56 1.00e-07 -2.5902668 -1.2640189 ***
Maciel °Brix b60 OsIs:60 11.0925000 10.8875000 0.2050000 56 56 3.91e-01 -0.2664532 0.6764532 ns
Maciel Firmness (N) f60 OsIs:60 3.6551786 3.9914286 -0.3362500 56 56 3.35e-01 -1.0247461 0.3522461 ns
Maciel DA index ida60 OsIs:60 1.2430909 1.3049091 -0.0618182 55 55 5.80e-01 -0.2825519 0.1589156 ns
Maciel Dry matter ms60 OsIs:60 15.1580357 14.7846429 0.3733929 56 56 5.06e-01 -0.7348816 1.4816673 ns
Maciel Titratable acidity ss60 OsIs:60 14.1375000 13.5466071 0.5908929 56 56 1.05e-01 -0.1249209 1.3067066 ns

2.2 Resumo numérico

# Mais recodificação.
v <- c("cor" = "Color (nm)",
       "le" = "Lesion size (mm)")

# Faz a recodificação.
tb_l <- tb_l %>%
    mutate(mea = recode(mea, !!!v))

# Medidas resumo.
tb_desc <- tb_l %>%
    filter(lado == "Is", str_detect(mea, "^[A-Z]")) %>%
    group_by(cultivar, ferimento, tempo, mea) %>%
    summarise_at("value", c("mean", "min", "max"), na.rm = TRUE)

# Lista para guardar as tabelas parciais.
tb_summary <- list()

# Variáveis numéricas.
tb_summary[[1]] <- tb_desc %>%
    mutate(string = sprintf("%0.1f (%0.1f; %0.1f)", mean, min, max)) %>%
    unite(col = "cond", cultivar, ferimento, sep = " ") %>%
    select(mea, tempo, cond, string) %>%
    spread(key = cond, value = string)

# Aparecimento de lesão (incidência).
tb_summary[[2]] <- tb_l %>%
    filter(lado == "Is", str_detect(mea, "Lesion")) %>%
    group_by(cultivar, ferimento, tempo) %>%
    summarise_at("value",
                 function(x) {
                     u <- sum(x > 0, na.rm = TRUE)
                     sprintf("%0.1f%% (%d/%d)",
                             100 * u/length(x),
                             u,
                             length(x))
                 }) %>%
    unite(col = "cond", cultivar, ferimento, sep = " ") %>%
    select(tempo, cond, value) %>%
    spread(key = cond, value = value) %>%
    add_column(mea = "Fruits with lesions", .before = 1)

# Esporulação (latência).
tb_summary[[3]] <- tb_l %>%
    filter(lado == "Is", mea == "la") %>%
    group_by(cultivar, ferimento, tempo) %>%
    summarise_at("value",
                 function(x) {
                     u <- sum(x > 0, na.rm = TRUE)
                     sprintf("%0.1f%% (%d/%d)",
                             100 * u/length(x),
                             u,
                             length(x))
                 }) %>%
    unite(col = "cond", cultivar, ferimento, sep = " ") %>%
    select(tempo, cond, value) %>%
    spread(key = cond, value = value) %>%
    add_column(mea = "Sporulated lesions", .before = 1)

# Junta as tabelas e renomeia variáveis.
tb_summary <- tb_summary %>%
    bind_rows() %>%
    rename("Variable" = "mea", "Time (h)" = "tempo")

cap <- "Physicochemical characteristics (medium, minimum and maximum values) and severity, incidence and latent period of *Monilinia fructicola* in wounded and not wounded fruit of ‘Chimarrita’ and ‘Maciel’ cultivar at postharvest period. Pelotas, RS, Brazil."

# Exibe.
knitr::kable(tb_summary, caption = cap)
Physicochemical characteristics (medium, minimum and maximum values) and severity, incidence and latent period of Monilinia fructicola in wounded and not wounded fruit of ‘Chimarrita’ and ‘Maciel’ cultivar at postharvest period. Pelotas, RS, Brazil.
Variable Time (h) Chimarrita noW Chimarrita W Maciel noW Maciel W
Color (nm) 0 84.9 (38.2; 112.1) 76.8 (24.7; 111.8) 97.6 (75.7; 111.8) 102.0 (74.0; 264.9)
DA index 0 1.5 (0.5; 2.1) 1.5 (0.9; 2.1) 1.5 (0.6; 2.1) 1.5 (0.3; 2.1)
DA index 48 1.2 (0.2; 2.1) 1.0 (0.3; 2.1) 1.3 (0.3; 2.3) 1.4 (0.3; 2.2)
DA index 60 1.0 (0.2; 2.1) 0.8 (0.2; 1.9) 1.2 (0.3; 2.1) 1.3 (0.4; 2.2)
Dry matter 0 9.8 (0.6; 16.2) 11.7 (1.3; 18.0) 15.4 (8.1; 19.8) 15.2 (5.8; 20.6)
Dry matter 48 14.1 (5.4; 19.3) 9.0 (0.7; 16.1) 18.1 (10.3; 24.9) 16.0 (7.3; 21.5)
Dry matter 60 14.4 (1.4; 19.0) 5.6 (0.2; 16.4) 15.4 (6.3; 20.8) 16.2 (7.9; 23.9)
Firmness (N) 0 5.8 (3.0; 6.7) 5.6 (3.6; 6.7) 5.6 (3.0; 9.1) 6.1 (3.0; 9.3)
Firmness (N) 48 4.4 (1.4; 6.3) 4.5 (-0.6; 8.2) 5.5 (3.1; 10.0) 4.6 (1.4; 8.8)
Firmness (N) 60 3.8 (1.2; 6.5) 5.3 (-0.1; 12.6) 3.9 (1.4; 8.5) 6.0 (1.9; 11.9)
Lesion size (mm) 48 0.0 (0.0; 0.0) 29.4 (24.8; 33.0) 0.0 (0.0; 0.0) 7.4 (0.0; 16.7)
Lesion size (mm) 60 0.0 (0.0; 0.0) 44.2 (37.7; 49.1) 0.0 (0.0; 0.0) 21.4 (0.0; 33.8)
Titratable acidity 0 7.1 (4.3; 10.3) 7.2 (3.9; 10.3) 12.0 (6.2; 15.0) 11.3 (6.9; 13.8)
Titratable acidity 48 7.1 (4.6; 11.5) 4.3 (1.1; 8.9) 12.2 (7.4; 15.3) 12.9 (6.4; 16.8)
Titratable acidity 60 5.9 (3.4; 10.3) -0.7 (-8.5; 7.2) 14.7 (6.5; 17.8) 7.8 (-2.2; 15.6)
Fruits with lesions 48 0.0% (0/56) 100.0% (56/56) 0.0% (0/56) 89.3% (50/56)
Fruits with lesions 60 0.0% (0/56) 100.0% (56/56) 0.0% (0/56) 96.4% (54/56)
Sporulated lesions 48 0.0% (0/56) 32.1% (18/56) 0.0% (0/56) 1.8% (1/56)
Sporulated lesions 60 0.0% (0/56) 100.0% (56/56) 0.0% (0/56) 7.1% (4/56)

3 Ajuste de modelos

Lesion size data was submitted to linear regression as variable dependent. Soluble solids content, DA index, titratable acidity, pulp firmness and dry matter were used as independent variables, as also its first order interactions (\(p = 21\) variables, \(n = 56\)). Variable selections were performed by stepwise procedure based on the Akaike Information Criterion (AIC) using \(k = 3.84\) that is the 95th quantile of a chi-square random variable with 1 degree of freedom . This makes selection variables being performed at a 5% significance level using likelihood ratio tests. The mean lesion size was predicted with the selected independent variables.

Latency was submitted to generalized linear regression assuming binomial distribution, as it is a dichotomous response variable (0 or 1). This is also known as logistic regression. The same variables were used as independent variable and selected using stepwise procedure based on the AIC with \(k = 3.84\). To prevent over fitting, since a dichotomous is less informative than a continous variable, only main effects terms were used (\(p = 6\) variables, \(n = 56\)). The probability about sporulated lesions was predicted with the selected independent variables.

All statistical procedures were done using a 0.05 nominal significance level. Statistical analysis was performed using the R software (R Core Team 2020).

Incluir como referência biliográfica:

R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

3.1 Tamanho de lesão

3.1.1 Chimarrita

# Seleciona recorte de interesse.
tb_reg <- tb %>%
    filter(cultivar == "Chimarrita", ferimento == "W", lado == "Is") %>%
    select(matches("[a-z]0"), le48, le60)

# Conta os valores ausentes.
tb_reg %>%
    summarise_all(~sum(is.na(.)))
## # A tibble: 1 × 8
##    cor0  ida0   ms0   ss0    f0    b0  le48  le60
##   <int> <int> <int> <int> <int> <int> <int> <int>
## 1     0     0    11     0     0     0     0     0
# Análise exploratória.
tb_reg %>%
    gather(key = "pred", value = "value", 1:6) %>%
    ggplot(mapping = aes(x = value, y = le60)) +
    facet_wrap(facets = ~pred, scale = "free_x") +
    geom_point() +
    geom_smooth(se = FALSE, color = "gray40") +
    labs(x = "Variável independente",
         y = "Tamanho da lesão")
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

# O modelo saturado com termos de primeira e segunda ordem.
m0 <- lm(le60 ~ (.)^2, data = select(tb_reg, -le48))
summary(m0)
## 
## Call:
## lm(formula = le60 ~ (.)^2, data = select(tb_reg, -le48))
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.660 -1.095 -0.019  1.151  4.655 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  14.417965 113.790988   0.127    0.900
## cor0         -0.100425   0.415863  -0.241    0.811
## ida0         80.314245  97.846660   0.821    0.420
## ms0           0.776230   5.575387   0.139    0.890
## ss0          -5.499361  14.524228  -0.379    0.708
## f0          -18.150884  36.111788  -0.503    0.620
## b0            6.655332   9.752256   0.682    0.502
## cor0:ida0     0.062521   0.160134   0.390    0.700
## cor0:ms0      0.011533   0.009462   1.219    0.235
## cor0:ss0     -0.021260   0.031717  -0.670    0.509
## cor0:f0       0.027501   0.068893   0.399    0.693
## cor0:b0      -0.010656   0.033846  -0.315    0.756
## ida0:ms0     -0.361286   1.400180  -0.258    0.799
## ida0:ss0     -3.148286   6.746582  -0.467    0.645
## ida0:f0       2.852293   8.168038   0.349    0.730
## ida0:b0      -5.693814   7.833365  -0.727    0.475
## ms0:ss0      -0.454088   0.526190  -0.863    0.397
## ms0:f0        0.866997   1.275913   0.680    0.504
## ms0:b0       -0.188244   0.320390  -0.588    0.563
## ss0:f0        1.177671   2.042980   0.576    0.570
## ss0:b0        0.864472   1.530276   0.565    0.578
## f0:b0        -0.482836   1.646729  -0.293    0.772
## 
## Residual standard error: 2.234 on 23 degrees of freedom
##   (11 observations deleted due to missingness)
## Multiple R-squared:  0.4762, Adjusted R-squared:  -0.001969 
## F-statistic: 0.9959 on 21 and 23 DF,  p-value: 0.5012
# Aplica o stepwise para selecionar variáveis.
# Aqui usa-se AIC com k = 3.84.
m1 <- step(update(m0, data = m0$model),
           k = qchisq(0.95, df = 1),
           trace = 0,
           data = m0$model)
summary(m1)
## 
## Call:
## lm(formula = le60 ~ cor0 + ms0 + ss0 + b0 + cor0:ms0, data = m0$model)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.6754 -1.2921  0.2102  1.3962  4.0627 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 54.009190   5.126397  10.536 5.72e-13 ***
## cor0        -0.089881   0.040391  -2.225   0.0319 *  
## ms0         -0.293178   0.283065  -1.036   0.3067    
## ss0          1.011585   0.388371   2.605   0.0129 *  
## b0          -1.018524   0.370448  -2.749   0.0090 ** 
## cor0:ms0     0.008129   0.003374   2.409   0.0208 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.982 on 39 degrees of freedom
## Multiple R-squared:  0.3009, Adjusted R-squared:  0.2112 
## F-statistic: 3.357 on 5 and 39 DF,  p-value: 0.01287
# Testa o não comprometimento dos termos abandonados.
anova(m0, m1)
## Analysis of Variance Table
## 
## Model 1: le60 ~ (cor0 + ida0 + ms0 + ss0 + f0 + b0)^2
## Model 2: le60 ~ cor0 + ms0 + ss0 + b0 + cor0:ms0
##   Res.Df    RSS  Df Sum of Sq      F Pr(>F)
## 1     23 114.78                            
## 2     39 153.21 -16    -38.43 0.4813 0.9321
par(mfrow = c(2, 2))
plot(m1); layout(1)

O modelo obtido com stepwise contém 4 variáveis, incluindo a interação entre um par delas. 11 observações foram eliminadas por causa de valores ausentes na variáveis ms0. Então o modelo foi ajustado com 45.

Apesar do baixo \(R^2\), o efeito das variáveis é significativo a 5%. O baixo \(R^2\) apenas indica que tais variáveis explicam uma pequena porção da variabilidade total.

Não observou-se nenhum afastamento dos pressupostos do modelo de regressão por meio da análise gráfica dos resíduos.

O sinal dos coeficientes estimados indica se o efeito da variável é positivo ou negativo no tamanho da lesão. Cuidado ao interpretar efeitos principais de variáveis envolvidas em interações.

# Prepara malha para a predição.
# summary(m1$model)
tb_pred <- with(m1$model,
                crossing(cor0 = seq(min(cor0), max(cor0), length.out = 24),
                         ms0 = seq(min(ms0), max(ms0), length.out = 24),
                         b0 = c(11, 12, 13),
                         ss0 = c(5, 6, 7)))
str(tb_pred)
## tibble [5,184 × 4] (S3: tbl_df/tbl/data.frame)
##  $ cor0: num [1:5184] 24.7 24.7 24.7 24.7 24.7 ...
##  $ ms0 : num [1:5184] 1.31 1.31 1.31 1.31 1.31 ...
##  $ b0  : num [1:5184] 11 11 11 12 12 12 13 13 13 11 ...
##  $ ss0 : num [1:5184] 5 6 7 5 6 7 5 6 7 5 ...
# Predição de cada ponto.
tb_pred$fit <- predict(m1, newdata = tb_pred)
cap <- "Lesion size at 60 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Maciel cultivar."

# Gráfico de contornos de nível.
ggplot(data = tb_pred,
       mapping = aes(x = cor0, y = ms0, fill = fit)) +
    facet_grid(facets = b0 ~ ss0) +
    geom_tile() +
    geom_contour(mapping = aes(z = fit), color = "black") +
    scale_fill_distiller(palette = "Spectral") +
    labs(x = "Color",
         y = "Dry matter",
         fill = "Lesion\nsize (mm)",
         title = "°Brix (rows) x Titratable acidity (columns)")
Lesion size at 60 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Maciel cultivar.

Lesion size at 60 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Maciel cultivar. 

# Gráfico 3D.
useOuterStrips(
    wireframe(fit ~ cor0 + ms0 |  factor(ss0) + factor(b0),
              data = tb_pred,
              drape = TRUE, col.regions = my_palette(90),
              scales = list(arrows = FALSE),
              par.settings = list(strip.background =
                                      list(col = c("gray90","gray50")),
                                  par.main.text = list(font = 1,
                                                       just = "left",
                                                       x = grid::unit(10, "mm"))),
              main = list("°Brix (rows) x Titratable acidity (columns)"),
              xlab = list("Color", rot = 30),
              ylab = list("Dry matter", rot = -40),
              zlab = list("Lesion size", rot = 90)))
Lesion size at 60 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Maciel cultivar.

Lesion size at 60 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Maciel cultivar.

Os gráficos mostram que os maiores tamanho de lesão são esperados para a combinação de valores altos de dry matter com valores altos de color. Mantida as demais variáveis contantes, o aumento de total soluble solids diminui o tamanho de lesão enquanto que o aumento de brix provoca aumento no tamanho da lesão.

3.1.2 Maciel

# Seleciona recorte de interesse.
tb_reg <- tb %>%
    filter(cultivar == "Maciel", ferimento == "W", lado == "Is") %>%
    mutate(cor0 = if_else(cor0 > 150, NA_real_, cor0)) %>%
    select(matches("[a-z]0"), le48, le60)

# Conta os valores ausentes.
tb_reg %>%
    summarise_all(~sum(is.na(.)))
## # A tibble: 1 × 8
##    cor0  ida0   ms0   ss0    f0    b0  le48  le60
##   <int> <int> <int> <int> <int> <int> <int> <int>
## 1     1     0     0     0     0     0     1     0
# Análise exploratória.
tb_reg %>%
    gather(key = "pred", value = "value", 1:6) %>%
    ggplot(mapping = aes(x = value, y = le60)) +
    facet_wrap(facets = ~pred, scale = "free_x") +
    geom_point() +
    geom_smooth(se = FALSE, color = "gray40") +
    labs(x = "Variável independente",
         y = "Tamanho da lesão")
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

# O modelo saturado com termos de primeira e segunda ordem.
m0 <- lm(le60 ~ (.)^2, data = select(tb_reg, -le48))
summary(m0)
## 
## Call:
## lm(formula = le60 ~ (.)^2, data = select(tb_reg, -le48))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -16.594  -3.728   1.204   4.750  11.392 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  3.249e+02  5.302e+02   0.613   0.5443  
## cor0        -3.255e+00  5.146e+00  -0.632   0.5314  
## ida0         6.992e+02  2.765e+02   2.529   0.0164 *
## ms0          1.526e+00  2.200e+01   0.069   0.9451  
## ss0         -2.991e+01  3.433e+01  -0.871   0.3899  
## f0          -1.786e+02  8.014e+01  -2.229   0.0327 *
## b0           3.059e+00  5.138e+01   0.060   0.9529  
## cor0:ida0   -4.729e+00  2.063e+00  -2.293   0.0284 *
## cor0:ms0     5.955e-02  2.090e-01   0.285   0.7775  
## cor0:ss0     1.050e-01  2.792e-01   0.376   0.7092  
## cor0:f0      1.418e+00  5.854e-01   2.423   0.0211 *
## cor0:b0      1.379e-02  5.077e-01   0.027   0.9785  
## ida0:ms0    -1.113e+01  4.501e+00  -2.473   0.0187 *
## ida0:ss0     3.988e+00  6.868e+00   0.581   0.5654  
## ida0:f0     -5.590e+00  5.451e+00  -1.026   0.3126  
## ida0:b0     -8.047e+00  7.120e+00  -1.130   0.2665  
## ms0:ss0      5.896e-01  6.676e-01   0.883   0.3836  
## ms0:f0       2.164e+00  1.482e+00   1.460   0.1537  
## ms0:b0      -7.514e-01  7.464e-01  -1.007   0.3214  
## ss0:f0       6.265e-03  1.498e+00   0.004   0.9967  
## ss0:b0       4.486e-01  1.291e+00   0.347   0.7305  
## f0:b0        1.606e+00  2.867e+00   0.560   0.5792  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.464 on 33 degrees of freedom
##   (1 observation deleted due to missingness)
## Multiple R-squared:  0.3728, Adjusted R-squared:  -0.02638 
## F-statistic: 0.9339 on 21 and 33 DF,  p-value: 0.5564
# Aplica o stepwise para selecionar variáveis.
# Aqui usa-se AIC com k = 3.84.
m1 <- step(update(m0, data = m0$model),
           k = qchisq(0.95, df = 1),
           trace = 0,
           data = m0$model)
summary(m1)
## 
## Call:
## lm(formula = le60 ~ 1, data = m0$model)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -21.237  -4.742   1.723   6.373  12.603 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   21.237      1.127   18.85   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.355 on 54 degrees of freedom
# Testa o não comprometimento dos termos abandonados.
anova(m0, m1)
## Analysis of Variance Table
## 
## Model 1: le60 ~ (cor0 + ida0 + ms0 + ss0 + f0 + b0)^2
## Model 2: le60 ~ 1
##   Res.Df    RSS  Df Sum of Sq      F Pr(>F)
## 1     33 2364.4                            
## 2     54 3769.5 -21   -1405.1 0.9339 0.5564

Para a cultivar Maciel, não se conseguiu modelo útil. O procedimento stepwise saiu do modelo saturado (\(p = 21\)) e obteve o modelo nulo (aapenas intercepto). Portanto, nenhum dos modelos avaliados superou significativamente o modelo nulo. Dessa forma, não foi possível detectar efeito das variáveis independentes no tamanho de lesão para a cultivar Maciel. Há pelo duas razões para a falha na detecção de efeito (caso ele exista): 1) o tamanho de amostra não foi suficiente e 2) as variáveis preditoras apresentaram valores numa faixa estreita do domínio que não permite “capturar o sinal” de seu efeito na resposta. Em futuros experimentos pode-se aumentar o tamanho de amostra e priorizar a seleção de frutos com valores mais extremos nas variáveis preditoras para ampliar o domínio observado delas.

3.2 Latência

3.2.1 Chimarrita

# Seleciona recorte de interesse.
tb_reg <- tb %>%
    filter(cultivar == "Chimarrita", ferimento == "W", lado == "Is") %>%
    select(matches("[a-z]0"), la48, la60)

# Conta os valores ausentes.
tb_reg %>%
    summarise_all(~sum(is.na(.)))
## # A tibble: 1 × 8
##    cor0  ida0   ms0   ss0    f0    b0  la48  la60
##   <int> <int> <int> <int> <int> <int> <int> <int>
## 1     0     0    11     0     0     0     0     0
# Análise exploratória.
tb_reg %>%
    gather(key = "pred", value = "value", 1:6) %>%
    ggplot(mapping = aes(x = value, y = la48)) +
    facet_wrap(facets = ~pred, scale = "free_x") +
    geom_point() +
    geom_smooth(se = FALSE, color = "gray40") +
    labs(x = "Variável independente",
         y = "Tamanho da lesão")
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

# Resumo descritivo.
summary(tb_reg)
##       cor0             ida0            ms0             ss0        
##  Min.   : 24.66   Min.   :0.870   Min.   : 1.31   Min.   : 3.880  
##  1st Qu.: 50.17   1st Qu.:1.278   1st Qu.:10.23   1st Qu.: 6.133  
##  Median : 80.65   Median :1.480   Median :12.04   Median : 7.200  
##  Mean   : 76.82   Mean   :1.526   Mean   :11.68   Mean   : 7.237  
##  3rd Qu.:105.59   3rd Qu.:1.752   3rd Qu.:14.18   3rd Qu.: 8.002  
##  Max.   :111.79   Max.   :2.100   Max.   :17.96   Max.   :10.340  
##                                   NA's   :11                      
##        f0              b0             la48             la60  
##  Min.   :3.560   Min.   : 9.41   Min.   :0.0000   Min.   :1  
##  1st Qu.:5.435   1st Qu.:11.54   1st Qu.:0.0000   1st Qu.:1  
##  Median :5.740   Median :12.21   Median :0.0000   Median :1  
##  Mean   :5.648   Mean   :12.22   Mean   :0.3214   Mean   :1  
##  3rd Qu.:6.085   3rd Qu.:12.79   3rd Qu.:1.0000   3rd Qu.:1  
##  Max.   :6.730   Max.   :14.60   Max.   :1.0000   Max.   :1  
## 
# Frequências da resposta.
tb_reg %>%
    count(la48, la60)
## # A tibble: 2 × 3
##    la48  la60     n
##   <dbl> <dbl> <int>
## 1     0     1    38
## 2     1     1    18
# O modelo saturado com termos de primeira ordem.
# Para prevenir over fitting, usou-se apenas termos de primeira ordem.
m0 <- glm(la48 ~ .,
          family = binomial,
          data = select(tb_reg, -la60))
summary(m0)
## 
## Call:
## glm(formula = la48 ~ ., family = binomial, data = select(tb_reg, 
##     -la60))
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.7493  -0.5315  -0.1571   0.5991   2.8952  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)   
## (Intercept) 17.27344    7.46018   2.315  0.02059 * 
## cor0         0.03543    0.02167   1.635  0.10211   
## ida0        -7.57770    4.65720  -1.627  0.10372   
## ms0          0.66842    0.29587   2.259  0.02387 * 
## ss0          0.65159    0.73261   0.889  0.37379   
## f0           2.15013    1.49040   1.443  0.14912   
## b0          -2.78565    0.95487  -2.917  0.00353 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 60.571  on 44  degrees of freedom
## Residual deviance: 35.100  on 38  degrees of freedom
##   (11 observations deleted due to missingness)
## AIC: 49.1
## 
## Number of Fisher Scoring iterations: 6
# Testa o modelo nulo contra o modelo saturado.
mnull <- update(m0, formula = . ~ 1, data = m0$model)
anova(mnull, m0, test = "Chisq")
## Analysis of Deviance Table
## 
## Model 1: la48 ~ 1
## Model 2: la48 ~ cor0 + ida0 + ms0 + ss0 + f0 + b0
##   Resid. Df Resid. Dev Df Deviance  Pr(>Chi)    
## 1        44     60.571                          
## 2        38     35.100  6   25.471 0.0002792 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Aplica o stepwise para selecionar variáveis.
# Aqui usa-se AIC com k = 3.84.
m1 <- step(update(m0, data = m0$model),
           k = qchisq(0.95, df = 1),
           trace = 0)
summary(m1)
## 
## Call:
## glm(formula = la48 ~ ms0 + b0, family = binomial, data = m0$model)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.7032  -0.7427  -0.3261   0.7290   2.2116  
## 
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)   
## (Intercept)  13.8716     5.2831   2.626  0.00865 **
## ms0           0.5167     0.1734   2.980  0.00288 **
## b0           -1.6543     0.5307  -3.117  0.00183 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 60.571  on 44  degrees of freedom
## Residual deviance: 42.571  on 42  degrees of freedom
## AIC: 48.571
## 
## Number of Fisher Scoring iterations: 5
# Testa o não comprometimento dos termos abandonados.
anova(m0, m1, test = "Chisq")
## Analysis of Deviance Table
## 
## Model 1: la48 ~ cor0 + ida0 + ms0 + ss0 + f0 + b0
## Model 2: la48 ~ ms0 + b0
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1        38     35.100                     
## 2        42     42.571 -4  -7.4714    0.113
# Acurácia.
sum(m1$model$la48 == (fitted(m1) > 0.5))/nrow(m1$model)
## [1] 0.7777778
# Diagnóstico.
par(mfrow = c(2, 2))
plot(m1); layout(1)

O procedimento stepwise obteve um modelo com duas variáveis. Não observou-se afastamento dos pressupostos. A acurácia foi 77%.

# Prepara malha para a predição.
# summary(m1$model)
tb_pred <- with(m1$model,
                crossing(b0 = seq(min(b0), max(b0), length.out = 24),
                         ms0 = seq(min(ms0), max(ms0), length.out = 24)))
str(tb_pred)
## tibble [576 × 2] (S3: tbl_df/tbl/data.frame)
##  $ b0 : num [1:576] 9.41 9.41 9.41 9.41 9.41 9.41 9.41 9.41 9.41 9.41 ...
##  $ ms0: num [1:576] 1.31 2.03 2.76 3.48 4.21 ...
# Predição de cada ponto.
tb_pred$fit <- predict(m1, newdata = tb_pred, type = "response")
cap <- "Latency at 48 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Chimarrita cultivar."

# Gráfico de contornos de nível.
ggplot(data = tb_pred,
       mapping = aes(x = b0, y = ms0, fill = fit)) +
    geom_tile() +
    geom_contour(mapping = aes(z = fit), color = "black") +
    scale_fill_distiller(palette = "Spectral") +
    labs(x = "°Brix",
         y = "Dry matter",
         fill = "Prob.\nlatency")
Latency at 48 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Chimarrita cultivar.

Latency at 48 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Chimarrita cultivar. 

# Gráfico 3D.
wireframe(fit ~ b0 + ms0,
          data = tb_pred,
          drape = TRUE, col.regions = my_palette(90),
          scales = list(arrows = FALSE),
          xlab = list("°Brix", rot = 30),
          ylab = list("Dry matter", rot = -40),
          zlab = list("Prob. latency", rot = 90))
Latency at 48 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Chimarrita cultivar.

Latency at 48 h for wounded inoculated fruits predicted as a function of variables measured at inoculation (0 h) and select by stepwise procedure to Chimarrita cultivar.

O gráfico para a probabilidade de esporulação do fruto mostra que há aumento na probabilidade de esporulação com aumento da dry matter e diminuição do brix.

3.2.2 Maciel

# Seleciona recorte de interesse.
tb_reg <- tb %>%
    filter(cultivar == "Maciel", ferimento == "W", lado == "Is") %>%
    select(matches("[a-z]0"), la48, la60)

# Conta os valores ausentes.
tb_reg %>%
    summarise_all(~sum(is.na(.)))
## # A tibble: 1 × 8
##    cor0  ida0   ms0   ss0    f0    b0  la48  la60
##   <int> <int> <int> <int> <int> <int> <int> <int>
## 1     0     0     0     0     0     0     0     0
# Análise exploratória.
tb_reg %>%
    gather(key = "pred", value = "value", 1:6) %>%
    ggplot(mapping = aes(x = value, y = la48)) +
    facet_wrap(facets = ~pred, scale = "free_x") +
    geom_point() +
    geom_smooth(se = FALSE, color = "gray40") +
    labs(x = "Variável independente",
         y = "Tamanho da lesão")
## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'

# Resumo descritivo.
summary(tb_reg)
##       cor0             ida0            ms0             ss0       
##  Min.   : 73.99   Min.   :0.330   Min.   : 5.75   Min.   : 6.87  
##  1st Qu.: 94.08   1st Qu.:1.208   1st Qu.:12.37   1st Qu.:10.39  
##  Median : 99.65   Median :1.630   Median :15.87   Median :11.64  
##  Mean   :102.05   Mean   :1.544   Mean   :15.15   Mean   :11.29  
##  3rd Qu.:106.57   3rd Qu.:2.005   3rd Qu.:18.00   3rd Qu.:12.54  
##  Max.   :264.85   Max.   :2.150   Max.   :20.58   Max.   :13.82  
##        f0              b0             la48              la60        
##  Min.   :2.990   Min.   : 9.70   Min.   :0.00000   Min.   :0.00000  
##  1st Qu.:4.543   1st Qu.:10.76   1st Qu.:0.00000   1st Qu.:0.00000  
##  Median :5.880   Median :11.64   Median :0.00000   Median :0.00000  
##  Mean   :6.057   Mean   :11.68   Mean   :0.01786   Mean   :0.07143  
##  3rd Qu.:7.700   3rd Qu.:12.49   3rd Qu.:0.00000   3rd Qu.:0.00000  
##  Max.   :9.310   Max.   :13.88   Max.   :1.00000   Max.   :1.00000
# Frequências da resposta.
tb_reg %>%
    count(la48, la60)
## # A tibble: 3 × 3
##    la48  la60     n
##   <dbl> <dbl> <int>
## 1     0     0    52
## 2     0     1     3
## 3     1     1     1

Não foi possível obter modelo para a latência para a cultivar Maciel pois houve um grande e impeditivo desequilíbrio de classe na variável desfecho. Isso porque com 48 e 60 horas observou-se apenas alguns frutos com esporulação. Talvez se o período de observação fosse prolongado, poderia-se ter mais frutos esporulados para permitir ajustar o modelo. Nos próximos experimentos pode-se usar o critério de encerrar o experimento apenas quando 50% dos frutos apresentar esporulação.