RTE fruit stats
2018/05/25
Spreadsheet notes
The file “data_allfruits.xlsx” contains all raw values for L. monocytogenes counts and TVC. The file “data_allfruits.gp.xlsx” contains the growth potential values for L. monocytogenes at each time point. LM represents the CFU counts for Listeria monocytogenes, PC represents the total viable count on plate count agar.
library(lmerTest)## Loading required package: lme4## Loading required package: Matrix##
## Attaching package: 'lmerTest'## The following object is masked from 'package:lme4':
##
## lmer## The following object is masked from 'package:stats':
##
## steplibrary(readxl)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(lsmeans)## The 'lsmeans' package is being deprecated.
## Users are encouraged to switch to 'emmeans'.
## See help('transition') for more information, including how
## to convert 'lsmeans' objects and scripts to work with 'emmeans'.library(tidyr)##
## Attaching package: 'tidyr'## The following object is masked from 'package:Matrix':
##
## expandlibrary(reshape2)##
## Attaching package: 'reshape2'## The following object is masked from 'package:tidyr':
##
## smithslibrary(car)## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodelibrary(effects)## lattice theme set by effectsTheme()
## See ?effectsTheme for details.library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## selectlibrary(ggplot2)
library(knitr)
library(kableExtra)
#GET AND ORGANIZE DATA
data.1 <- read_excel("./data/data_allfruits.gp.xlsx")
data.2 <- read_excel("./data/data_allfruits.xlsx")
#add log of CFU
data.2$logLM <- log10(data.2$LM)
data.2$logPC <- log10(data.2$PC)
#exclude negative control values. They are contamination controls. They
#can not provide any meaningful data to the response variable "logLM" because they
#have no logLM.
data.2 = data.2[!data.2$strain == "negative control",]
#Join salad and rep to make a factor unique for each salad/rep combo
data.2$salad_rep <- paste(data.2$product,data.2$replicate,data.2$temp)
#Print the data
data.1 %>%
kable("html") %>%
kable_styling(bootstrap_options=c("striped",
"hover",
"condensed",
"responsive"))| fruit | temp. | t | pH | gp | rep |
|---|---|---|---|---|---|
| Fruit mix 2 | 4 C - 8 C | 0 | 4.2 | 0.0000000 | 1-3 |
| Fruit mix 2 | 4 C - 8 C | 3 | 4.2 | 0.1361109 | 1-3 |
| Fruit mix 2 | 4 C - 8 C | 4 | 4.2 | 0.3979400 | 1-3 |
| Fruit mix 2 | 4 C - 8 C | 5 | 4.2 | 0.5199344 | 1-3 |
| Fruit mix 2 | 4 C - 8 C | 6 | 4.2 | 0.9156791 | 1-3 |
| Fruit mix 2 | 4 C - 12 C | 0 | 4.2 | 0.0000000 | 1-3 |
| Fruit mix 2 | 4 C - 12 C | 3 | 4.2 | 0.1463301 | 1-3 |
| Fruit mix 2 | 4 C - 12 C | 4 | 4.2 | 0.9503122 | 1-3 |
| Fruit mix 2 | 4 C - 12 C | 5 | 4.2 | 1.0274094 | 1-3 |
| Fruit mix 2 | 4 C - 12 C | 6 | 4.2 | 1.0659853 | 1-3 |
| Fruit mix 1 | 4 C - 8 C | 0 | 3.4 | 0.0000000 | 1-3 |
| Fruit mix 1 | 4 C - 8 C | 3 | 3.4 | 0.0579919 | 1-3 |
| Fruit mix 1 | 4 C - 8 C | 4 | 3.4 | 0.1103567 | 1-3 |
| Fruit mix 1 | 4 C - 8 C | 5 | 3.4 | 0.1390114 | 1-3 |
| Fruit mix 1 | 4 C - 8 C | 6 | 3.4 | 0.1017989 | 1-3 |
| Fruit mix 1 | 4 C - 12 C | 0 | 3.4 | 0.0000000 | 1-3 |
| Fruit mix 1 | 4 C - 12 C | 3 | 3.4 | 0.1017989 | 1-3 |
| Fruit mix 1 | 4 C - 12 C | 4 | 3.4 | 0.0941700 | 1-3 |
| Fruit mix 1 | 4 C - 12 C | 5 | 3.4 | 0.0403983 | 1-3 |
| Fruit mix 1 | 4 C - 12 C | 6 | 3.4 | 0.1788141 | 1-3 |
| Cantaloupe | 4 C - 8 C | 0 | 5.6 | 0.0000000 | 1-3 |
| Cantaloupe | 4 C - 8 C | 3 | 5.6 | 1.2317420 | 1-3 |
| Cantaloupe | 4 C - 8 C | 4 | 5.6 | 2.0373714 | 1-3 |
| Cantaloupe | 4 C - 8 C | 5 | 5.6 | 2.6455012 | 1-3 |
| Cantaloupe | 4 C - 8 C | 6 | 5.6 | 2.5555032 | 1-3 |
| Cantaloupe | 4 C - 12 C | 0 | 5.6 | 0.0000000 | 1-3 |
| Cantaloupe | 4 C - 12 C | 3 | 5.6 | 1.2936480 | 1-3 |
| Cantaloupe | 4 C - 12 C | 4 | 5.6 | 2.7296855 | 1-3 |
| Cantaloupe | 4 C - 12 C | 5 | 5.6 | 2.7936154 | 1-3 |
| Cantaloupe | 4 C - 12 C | 6 | 5.6 | 2.6041086 | 1-3 |
| Fruit mix 3 | 4 C - 8 C | 0 | 3.9 | 0.0000000 | 1-3 |
| Fruit mix 3 | 4 C - 8 C | 3 | 3.9 | 0.1930224 | 1-3 |
| Fruit mix 3 | 4 C - 8 C | 4 | 3.9 | 0.1482101 | 1-3 |
| Fruit mix 3 | 4 C - 8 C | 5 | 3.9 | 0.1537105 | 1-3 |
| Fruit mix 3 | 4 C - 8 C | 6 | 3.9 | 0.1575501 | 1-3 |
| Fruit mix 3 | 4 C - 12 C | 0 | 3.9 | 0.0000000 | 1-3 |
| Fruit mix 3 | 4 C - 12 C | 3 | 3.9 | 0.1189484 | 1-3 |
| Fruit mix 3 | 4 C - 12 C | 4 | 3.9 | 0.2085591 | 1-3 |
| Fruit mix 3 | 4 C - 12 C | 5 | 3.9 | 0.4585801 | 1-3 |
| Fruit mix 3 | 4 C - 12 C | 6 | 3.9 | 0.4154307 | 1-3 |
| Coconut | 4 C - 8 C | 0 | 6.4 | 0.0000000 | 1-3 |
| Coconut | 4 C - 8 C | 3 | 6.4 | 1.2552725 | 1-3 |
| Coconut | 4 C - 8 C | 4 | 6.4 | 3.0010763 | 1-3 |
| Coconut | 4 C - 8 C | 5 | 6.4 | 3.0381476 | 1-3 |
| Coconut | 4 C - 8 C | 6 | 6.4 | 3.6251439 | 1-3 |
| Coconut | 4 C - 12 C | 0 | 6.4 | 0.0000000 | 1-3 |
| Coconut | 4 C - 12 C | 3 | 6.4 | 1.3881802 | 1-3 |
| Coconut | 4 C - 12 C | 4 | 6.4 | 2.6892102 | 1-3 |
| Coconut | 4 C - 12 C | 5 | 6.4 | 4.1926546 | 1-3 |
| Coconut | 4 C - 12 C | 6 | 6.4 | 4.7978155 | 1-3 |
| Mango | 4 C - 8 C | 0 | 3.6 | 0.0000000 | 1-3 |
| Mango | 4 C - 8 C | 3 | 3.6 | 0.1432423 | 1-3 |
| Mango | 4 C - 8 C | 4 | 3.6 | 0.1114920 | 1-3 |
| Mango | 4 C - 8 C | 5 | 3.6 | 0.0000000 | 1-3 |
| Mango | 4 C - 8 C | 6 | 3.6 | 0.1327769 | 1-3 |
| Mango | 4 C - 12 C | 0 | 3.6 | 0.0000000 | 1-3 |
| Mango | 4 C - 12 C | 3 | 3.6 | 0.0775003 | 1-3 |
| Mango | 4 C - 12 C | 4 | 3.6 | 0.0947863 | 1-3 |
| Mango | 4 C - 12 C | 5 | 3.6 | 0.0113548 | 1-3 |
| Mango | 4 C - 12 C | 6 | 3.6 | 0.0251430 | 1-3 |
data.2 %>%
kable("html") %>%
kable_styling(bootstrap_options=c("striped",
"hover",
"condensed",
"responsive"))| product | temp | t | pH.average | LM | replicate | strain | PC | logLM | logPC | salad_rep |
|---|---|---|---|---|---|---|---|---|---|---|
| Fruit mix 1 | 4C + 8C | 0 | 3.4 | 7350 | 1 | pool | 10750 | 3.866287 | 4.031409 | Fruit mix 1 1 4C + 8C |
| Fruit mix 1 | 4C + 12C | 0 | 3.4 | 7350 | 1 | pool | 10750 | 3.866287 | 4.031409 | Fruit mix 1 1 4C + 12C |
| Fruit mix 1 | 4C + 8C | 0 | 3.4 | 7950 | 2 | pool | 15250 | 3.900367 | 4.183270 | Fruit mix 1 2 4C + 8C |
| Fruit mix 1 | 4C + 12C | 0 | 3.4 | 7950 | 2 | pool | 15250 | 3.900367 | 4.183270 | Fruit mix 1 2 4C + 12C |
| Fruit mix 1 | 4C + 8C | 0 | 3.4 | 8350 | 3 | pool | 13000 | 3.921686 | 4.113943 | Fruit mix 1 3 4C + 8C |
| Fruit mix 1 | 4C + 12C | 0 | 3.4 | 8350 | 3 | pool | 13000 | 3.921686 | 4.113943 | Fruit mix 1 3 4C + 12C |
| Fruit mix 1 | 4C + 8C | 3 | 3.4 | 8400 | 1 | pool | 10250 | 3.924279 | 4.010724 | Fruit mix 1 1 4C + 8C |
| Fruit mix 1 | 4C + 12C | 3 | 3.4 | 7175 | 1 | pool | 11250 | 3.855822 | 4.051152 | Fruit mix 1 1 4C + 12C |
| Fruit mix 1 | 4C + 8C | 3 | 3.4 | 8775 | 2 | pool | 11750 | 3.943247 | 4.070038 | Fruit mix 1 2 4C + 8C |
| Fruit mix 1 | 4C + 12C | 3 | 3.4 | 10050 | 2 | pool | 11000 | 4.002166 | 4.041393 | Fruit mix 1 2 4C + 12C |
| Fruit mix 1 | 4C + 8C | 3 | 3.4 | 7050 | 3 | pool | 17000 | 3.848189 | 4.230449 | Fruit mix 1 3 4C + 8C |
| Fruit mix 1 | 4C + 12C | 3 | 3.4 | 8825 | 3 | pool | 14000 | 3.945715 | 4.146128 | Fruit mix 1 3 4C + 12C |
| Fruit mix 1 | 4C + 8C | 4 | 3.4 | 7600 | 1 | pool | 10750 | 3.880814 | 4.031409 | Fruit mix 1 1 4C + 8C |
| Fruit mix 1 | 4C + 12C | 4 | 3.4 | 7775 | 1 | pool | 25000 | 3.890700 | 4.397940 | Fruit mix 1 1 4C + 12C |
| Fruit mix 1 | 4C + 8C | 4 | 3.4 | 10250 | 2 | pool | 42750 | 4.010724 | 4.630936 | Fruit mix 1 2 4C + 8C |
| Fruit mix 1 | 4C + 12C | 4 | 3.4 | 9875 | 2 | pool | 44750 | 3.994537 | 4.650793 | Fruit mix 1 2 4C + 12C |
| Fruit mix 1 | 4C + 8C | 4 | 3.4 | 8825 | 3 | pool | 75750 | 3.945715 | 4.879383 | Fruit mix 1 3 4C + 8C |
| Fruit mix 1 | 4C + 12C | 4 | 3.4 | 9600 | 3 | pool | 352500 | 3.982271 | 5.547159 | Fruit mix 1 3 4C + 12C |
| Fruit mix 1 | 4C + 8C | 5 | 3.4 | 7025 | 1 | pool | 13250 | 3.846646 | 4.122216 | Fruit mix 1 1 4C + 8C |
| Fruit mix 1 | 4C + 12C | 5 | 3.4 | 7025 | 1 | pool | 60500 | 3.846646 | 4.781755 | Fruit mix 1 1 4C + 12C |
| Fruit mix 1 | 4C + 8C | 5 | 3.4 | 8025 | 2 | pool | 542500 | 3.904445 | 5.734400 | Fruit mix 1 2 4C + 8C |
| Fruit mix 1 | 4C + 12C | 5 | 3.4 | 8725 | 2 | pool | 1057500 | 3.940765 | 6.024280 | Fruit mix 1 2 4C + 12C |
| Fruit mix 1 | 4C + 8C | 5 | 3.4 | 11500 | 3 | pool | 422500 | 4.060698 | 5.625827 | Fruit mix 1 3 4C + 8C |
| Fruit mix 1 | 4C + 12C | 5 | 3.4 | 8000 | 3 | pool | 9825000 | 3.903090 | 6.992333 | Fruit mix 1 3 4C + 12C |
| Fruit mix 1 | 4C + 8C | 6 | 3.4 | 7775 | 1 | pool | 52500 | 3.890700 | 4.720159 | Fruit mix 1 1 4C + 8C |
| Fruit mix 1 | 4C + 12C | 6 | 3.4 | 8375 | 1 | pool | 622500 | 3.922985 | 5.794139 | Fruit mix 1 1 4C + 12C |
| Fruit mix 1 | 4C + 8C | 6 | 3.4 | 10050 | 2 | pool | 645000 | 4.002166 | 5.809560 | Fruit mix 1 2 4C + 8C |
| Fruit mix 1 | 4C + 12C | 6 | 3.4 | 12000 | 2 | pool | 7275000 | 4.079181 | 6.861833 | Fruit mix 1 2 4C + 12C |
| Fruit mix 1 | 4C + 8C | 6 | 3.4 | 6650 | 3 | pool | 2075000 | 3.822822 | 6.317018 | Fruit mix 1 3 4C + 8C |
| Fruit mix 1 | 4C + 12C | 6 | 3.4 | 7500 | 3 | pool | 15750000 | 3.875061 | 7.197281 | Fruit mix 1 3 4C + 12C |
| Fruit mix 3 | 4C + 8C | 0 | 3.9 | 9125 | 1 | pool | 19500 | 3.960233 | 4.290035 | Fruit mix 3 1 4C + 8C |
| Fruit mix 3 | 4C + 12C | 0 | 3.9 | 9125 | 1 | pool | 19500 | 3.960233 | 4.290035 | Fruit mix 3 1 4C + 12C |
| Fruit mix 3 | 4C + 8C | 0 | 3.8 | 8325 | 2 | pool | 10250 | 3.920384 | 4.010724 | Fruit mix 3 2 4C + 8C |
| Fruit mix 3 | 4C + 12C | 0 | 3.8 | 8325 | 2 | pool | 10250 | 3.920384 | 4.010724 | Fruit mix 3 2 4C + 12C |
| Fruit mix 3 | 4C + 8C | 0 | 4.1 | 8175 | 3 | pool | 17000 | 3.912488 | 4.230449 | Fruit mix 3 3 4C + 8C |
| Fruit mix 3 | 4C + 12C | 0 | 4.1 | 8175 | 3 | pool | 17000 | 3.912488 | 4.230449 | Fruit mix 3 3 4C + 12C |
| Fruit mix 3 | 4C + 8C | 3 | 3.9 | 11000 | 1 | pool | 34500 | 4.041393 | 4.537819 | Fruit mix 3 1 4C + 8C |
| Fruit mix 3 | 4C + 12C | 3 | 3.9 | 12000 | 1 | pool | 24250 | 4.079181 | 4.384712 | Fruit mix 3 1 4C + 12C |
| Fruit mix 3 | 4C + 8C | 3 | 3.8 | 7500 | 2 | pool | 11750 | 3.875061 | 4.070038 | Fruit mix 3 2 4C + 8C |
| Fruit mix 3 | 4C + 12C | 3 | 3.8 | 9475 | 2 | pool | 13750 | 3.976579 | 4.138303 | Fruit mix 3 2 4C + 12C |
| Fruit mix 3 | 4C + 8C | 3 | 4.1 | 12750 | 3 | pool | 15500 | 4.105510 | 4.190332 | Fruit mix 3 3 4C + 8C |
| Fruit mix 3 | 4C + 12C | 3 | 4.1 | 9075 | 3 | pool | 15000 | 3.957847 | 4.176091 | Fruit mix 3 3 4C + 12C |
| Fruit mix 3 | 4C + 8C | 4 | 3.9 | 12500 | 1 | pool | 52750 | 4.096910 | 4.722222 | Fruit mix 3 1 4C + 8C |
| Fruit mix 3 | 4C + 12C | 4 | 3.9 | 14750 | 1 | pool | 545000 | 4.168792 | 5.736396 | Fruit mix 3 1 4C + 12C |
| Fruit mix 3 | 4C + 8C | 4 | 3.8 | 6875 | 2 | pool | 14000 | 3.837273 | 4.146128 | Fruit mix 3 2 4C + 8C |
| Fruit mix 3 | 4C + 12C | 4 | 3.8 | 7150 | 2 | pool | 18750 | 3.854306 | 4.273001 | Fruit mix 3 2 4C + 12C |
| Fruit mix 3 | 4C + 8C | 4 | 4.1 | 11500 | 3 | pool | 27000 | 4.060698 | 4.431364 | Fruit mix 3 3 4C + 8C |
| Fruit mix 3 | 4C + 12C | 4 | 4.1 | 10000 | 3 | pool | 352500 | 4.000000 | 5.547159 | Fruit mix 3 3 4C + 12C |
| Fruit mix 3 | 4C + 8C | 5 | 3.9 | 13000 | 1 | pool | 102500 | 4.113943 | 5.010724 | Fruit mix 3 1 4C + 8C |
| Fruit mix 3 | 4C + 12C | 5 | 3.9 | 10750 | 1 | pool | 2300000 | 4.031409 | 6.361728 | Fruit mix 3 1 4C + 12C |
| Fruit mix 3 | 4C + 8C | 5 | 3.8 | 6800 | 2 | pool | 15750 | 3.832509 | 4.197281 | Fruit mix 3 2 4C + 8C |
| Fruit mix 3 | 4C + 12C | 5 | 3.8 | 7200 | 2 | pool | 74500 | 3.857333 | 4.872156 | Fruit mix 3 2 4C + 12C |
| Fruit mix 3 | 4C + 8C | 5 | 4.1 | 10250 | 3 | pool | 120000 | 4.010724 | 5.079181 | Fruit mix 3 3 4C + 8C |
| Fruit mix 3 | 4C + 12C | 5 | 4.1 | 23500 | 3 | pool | 1250000 | 4.371068 | 6.096910 | Fruit mix 3 3 4C + 12C |
| Fruit mix 3 | 4C + 8C | 6 | 3.9 | 10250 | 1 | pool | 155000 | 4.010724 | 5.190332 | Fruit mix 3 1 4C + 8C |
| Fruit mix 3 | 4C + 12C | 6 | 3.9 | 23750 | 1 | pool | 22000000 | 4.375664 | 7.342423 | Fruit mix 3 1 4C + 12C |
| Fruit mix 3 | 4C + 8C | 6 | 3.8 | 8275 | 2 | pool | 19250 | 3.917768 | 4.284431 | Fruit mix 3 2 4C + 8C |
| Fruit mix 3 | 4C + 12C | 6 | 3.8 | 2500 | 2 | pool | 590000 | 3.397940 | 5.770852 | Fruit mix 3 2 4C + 12C |
| Fruit mix 3 | 4C + 8C | 6 | 4.1 | 11750 | 3 | pool | 377500 | 4.070038 | 5.576917 | Fruit mix 3 3 4C + 8C |
| Fruit mix 3 | 4C + 12C | 6 | 4.1 | 14500 | 3 | pool | 5800000 | 4.161368 | 6.763428 | Fruit mix 3 3 4C + 12C |
| Coconut | 4C + 8C | 0 | 6.4 | 9525 | 1 | pool | 12250 | 3.978865 | 4.088136 | Coconut 1 4C + 8C |
| Coconut | 4C + 12C | 0 | 6.4 | 9525 | 1 | pool | 12250 | 3.978865 | 4.088136 | Coconut 1 4C + 12C |
| Coconut | 4C + 8C | 0 | 6.4 | 10075 | 2 | pool | 12500 | 4.003245 | 4.096910 | Coconut 2 4C + 8C |
| Coconut | 4C + 12C | 0 | 6.4 | 10075 | 2 | pool | 12500 | 4.003245 | 4.096910 | Coconut 2 4C + 12C |
| Coconut | 4C + 8C | 0 | 6.4 | 11250 | 3 | pool | 17250 | 4.051152 | 4.236789 | Coconut 3 4C + 8C |
| Coconut | 4C + 12C | 0 | 6.4 | 11250 | 3 | pool | 17250 | 4.051152 | 4.236789 | Coconut 3 4C + 12C |
| Coconut | 4C + 8C | 3 | 6.4 | 91250 | 1 | pool | 455000 | 4.960233 | 5.658011 | Coconut 1 4C + 8C |
| Coconut | 4C + 12C | 3 | 6.4 | 122500 | 1 | pool | 877500 | 5.088136 | 5.943247 | Coconut 1 4C + 12C |
| Coconut | 4C + 8C | 3 | 6.4 | 70250 | 2 | pool | 52250 | 4.846646 | 4.718086 | Coconut 2 4C + 8C |
| Coconut | 4C + 12C | 3 | 6.4 | 93750 | 2 | pool | 80500 | 4.971971 | 4.905796 | Coconut 2 4C + 12C |
| Coconut | 4C + 8C | 3 | 6.4 | 202500 | 3 | pool | 330000 | 5.306425 | 5.518514 | Coconut 3 4C + 8C |
| Coconut | 4C + 12C | 3 | 6.4 | 275000 | 3 | pool | 500000 | 5.439333 | 5.698970 | Coconut 3 4C + 12C |
| Coconut | 4C + 8C | 4 | 6.4 | 945000 | 1 | pool | 19500000 | 5.975432 | 7.290035 | Coconut 1 4C + 8C |
| Coconut | 4C + 12C | 4 | 6.4 | 4275000 | 1 | pool | 94250000 | 6.630936 | 7.974281 | Coconut 1 4C + 12C |
| Coconut | 4C + 8C | 4 | 6.4 | 10100000 | 2 | pool | 3600000 | 7.004321 | 6.556303 | Coconut 2 4C + 8C |
| Coconut | 4C + 12C | 4 | 6.4 | 882500 | 2 | pool | 24700000 | 5.945715 | 7.392697 | Coconut 2 4C + 12C |
| Coconut | 4C + 8C | 4 | 6.4 | 1150000 | 3 | pool | 53000000 | 6.060698 | 7.724276 | Coconut 3 4C + 8C |
| Coconut | 4C + 12C | 4 | 6.4 | 5500000 | 3 | pool | 111500000 | 6.740363 | 8.047275 | Coconut 3 4C + 12C |
| Coconut | 4C + 8C | 5 | 6.4 | 2800000 | 1 | pool | 227500000 | 6.447158 | 8.356981 | Coconut 1 4C + 8C |
| Coconut | 4C + 12C | 5 | 6.4 | 2175000 | 1 | pool | 127500000 | 6.337459 | 8.105510 | Coconut 1 4C + 12C |
| Coconut | 4C + 8C | 5 | 6.4 | 11000000 | 2 | pool | 470000000 | 7.041393 | 8.672098 | Coconut 2 4C + 8C |
| Coconut | 4C + 12C | 5 | 6.4 | 157000000 | 2 | pool | 570000000 | 8.195900 | 8.755875 | Coconut 2 4C + 12C |
| Coconut | 4C + 8C | 5 | 6.4 | 6325000 | 3 | pool | 255000000 | 6.801061 | 8.406540 | Coconut 3 4C + 8C |
| Coconut | 4C + 12C | 5 | 6.4 | 58500000 | 3 | pool | 1007500000 | 7.767156 | 9.003245 | Coconut 3 4C + 12C |
| Coconut | 4C + 8C | 6 | 6.4 | 9075000 | 1 | pool | 170000000 | 6.957847 | 8.230449 | Coconut 1 4C + 8C |
| Coconut | 4C + 12C | 6 | 6.4 | 63500000 | 1 | pool | 185000000 | 7.802774 | 8.267172 | Coconut 1 4C + 12C |
| Coconut | 4C + 8C | 6 | 6.4 | 42500000 | 2 | pool | 762500000 | 7.628389 | 8.882240 | Coconut 2 4C + 8C |
| Coconut | 4C + 12C | 6 | 6.4 | 632500000 | 2 | pool | 1775000000 | 8.801061 | 9.249198 | Coconut 2 4C + 12C |
| Coconut | 4C + 8C | 6 | 6.4 | 23500000 | 3 | pool | 535000000 | 7.371068 | 8.728354 | Coconut 3 4C + 8C |
| Coconut | 4C + 12C | 6 | 6.4 | 220000000 | 3 | pool | 687500000 | 8.342423 | 8.837273 | Coconut 3 4C + 12C |
| Fruit mix 2 | 4C + 8C | 0 | 4.2 | 8075 | 1 | pool | 11500 | 3.907142 | 4.060698 | Fruit mix 2 1 4C + 8C |
| Fruit mix 2 | 4C + 12C | 0 | 4.2 | 8075 | 1 | pool | 11500 | 3.907142 | 4.060698 | Fruit mix 2 1 4C + 12C |
| Fruit mix 2 | 4C + 8C | 0 | 3.9 | 7400 | 2 | pool | 11250 | 3.869232 | 4.051152 | Fruit mix 2 2 4C + 8C |
| Fruit mix 2 | 4C + 12C | 0 | 3.9 | 7400 | 2 | pool | 11250 | 3.869232 | 4.051152 | Fruit mix 2 2 4C + 12C |
| Fruit mix 2 | 4C + 8C | 0 | 3.8 | 7675 | 3 | pool | 9350 | 3.885078 | 3.970812 | Fruit mix 2 3 4C + 8C |
| Fruit mix 2 | 4C + 12C | 0 | 3.8 | 7675 | 3 | pool | 9350 | 3.885078 | 3.970812 | Fruit mix 2 3 4C + 12C |
| Fruit mix 2 | 4C + 8C | 3 | 4.2 | 5325 | 1 | pool | 8000 | 3.726320 | 3.903090 | Fruit mix 2 1 4C + 8C |
| Fruit mix 2 | 4C + 12C | 3 | 4.2 | 5425 | 1 | pool | 12000 | 3.734400 | 4.079181 | Fruit mix 2 1 4C + 12C |
| Fruit mix 2 | 4C + 8C | 3 | 3.9 | 8025 | 2 | pool | 17250 | 3.904445 | 4.236789 | Fruit mix 2 2 4C + 8C |
| Fruit mix 2 | 4C + 12C | 3 | 3.9 | 8900 | 2 | pool | 172500 | 3.949390 | 5.236789 | Fruit mix 2 2 4C + 12C |
| Fruit mix 2 | 4C + 8C | 3 | 3.8 | 10500 | 3 | pool | 11250 | 4.021189 | 4.051152 | Fruit mix 2 3 4C + 8C |
| Fruit mix 2 | 4C + 12C | 3 | 3.8 | 10750 | 3 | pool | 21500 | 4.031409 | 4.332439 | Fruit mix 2 3 4C + 12C |
| Fruit mix 2 | 4C + 8C | 4 | 4.2 | 8825 | 1 | pool | 25250 | 3.945715 | 4.402261 | Fruit mix 2 1 4C + 8C |
| Fruit mix 2 | 4C + 12C | 4 | 4.2 | 26250 | 1 | pool | 91500 | 4.419129 | 4.961421 | Fruit mix 2 1 4C + 12C |
| Fruit mix 2 | 4C + 8C | 4 | 3.9 | 18500 | 2 | pool | 810000 | 4.267172 | 5.908485 | Fruit mix 2 2 4C + 8C |
| Fruit mix 2 | 4C + 12C | 4 | 3.9 | 66000 | 2 | pool | 4330000 | 4.819544 | 6.636488 | Fruit mix 2 2 4C + 12C |
| Fruit mix 2 | 4C + 8C | 4 | 3.8 | 14750 | 3 | pool | 270000 | 4.168792 | 5.431364 | Fruit mix 2 3 4C + 8C |
| Fruit mix 2 | 4C + 12C | 4 | 3.8 | 14500 | 3 | pool | 525000 | 4.161368 | 5.720159 | Fruit mix 2 3 4C + 12C |
| Fruit mix 2 | 4C + 8C | 5 | 4.2 | 6325 | 1 | pool | 26250 | 3.801061 | 4.419129 | Fruit mix 2 1 4C + 8C |
| Fruit mix 2 | 4C + 12C | 5 | 4.2 | 52000 | 1 | pool | 200000 | 4.716003 | 5.301030 | Fruit mix 2 1 4C + 12C |
| Fruit mix 2 | 4C + 8C | 5 | 3.9 | 24500 | 2 | pool | 1350000 | 4.389166 | 6.130334 | Fruit mix 2 2 4C + 8C |
| Fruit mix 2 | 4C + 12C | 5 | 3.9 | 76750 | 2 | pool | 3975000 | 4.885078 | 6.599337 | Fruit mix 2 2 4C + 12C |
| Fruit mix 2 | 4C + 8C | 5 | 3.8 | 15750 | 3 | pool | 4125000 | 4.197281 | 6.615424 | Fruit mix 2 3 4C + 8C |
| Fruit mix 2 | 4C + 12C | 5 | 3.8 | 81750 | 3 | pool | 4525000 | 4.912488 | 6.655619 | Fruit mix 2 3 4C + 12C |
| Fruit mix 2 | 4C + 8C | 6 | 4.2 | 66500 | 1 | pool | 792500 | 4.822822 | 5.898999 | Fruit mix 2 1 4C + 8C |
| Fruit mix 2 | 4C + 12C | 6 | 4.2 | 94000 | 1 | pool | 4425000 | 4.973128 | 6.645913 | Fruit mix 2 1 4C + 12C |
| Fruit mix 2 | 4C + 8C | 6 | 3.9 | 11750 | 2 | pool | 1075000 | 4.070038 | 6.031409 | Fruit mix 2 2 4C + 8C |
| Fruit mix 2 | 4C + 12C | 6 | 3.9 | 43500 | 2 | pool | 2300000 | 4.638489 | 6.361728 | Fruit mix 2 2 4C + 12C |
| Fruit mix 2 | 4C + 8C | 6 | 3.8 | 14750 | 3 | pool | 2950000 | 4.168792 | 6.469822 | Fruit mix 2 3 4C + 8C |
| Fruit mix 2 | 4C + 12C | 6 | 3.8 | 34250 | 3 | pool | 2575000 | 4.534661 | 6.410777 | Fruit mix 2 3 4C + 12C |
| Mango | 4C + 8C | 0 | 3.6 | 7550 | 1 | pool | 8200 | 3.877947 | 3.913814 | Mango 1 4C + 8C |
| Mango | 4C + 12C | 0 | 3.6 | 7550 | 1 | pool | 8200 | 3.877947 | 3.913814 | Mango 1 4C + 12C |
| Mango | 4C + 8C | 0 | 3.8 | 8625 | 2 | pool | 10500 | 3.935759 | 4.021189 | Mango 2 4C + 8C |
| Mango | 4C + 12C | 0 | 3.8 | 8625 | 2 | pool | 10500 | 3.935759 | 4.021189 | Mango 2 4C + 12C |
| Mango | 4C + 8C | 0 | 4.3 | 10250 | 3 | pool | 11500 | 4.010724 | 4.060698 | Mango 3 4C + 8C |
| Mango | 4C + 12C | 0 | 4.3 | 10250 | 3 | pool | 11500 | 4.010724 | 4.060698 | Mango 3 4C + 12C |
| Mango | 4C + 8C | 3 | 3.6 | 10500 | 1 | pool | 16500 | 4.021189 | 4.217484 | Mango 1 4C + 8C |
| Mango | 4C + 12C | 3 | 3.6 | 9025 | 1 | pool | 11000 | 3.955447 | 4.041393 | Mango 1 4C + 12C |
| Mango | 4C + 8C | 3 | 3.8 | 7575 | 2 | pool | 12250 | 3.879383 | 4.088136 | Mango 2 4C + 8C |
| Mango | 4C + 12C | 3 | 3.8 | 8950 | 2 | pool | 14250 | 3.951823 | 4.153815 | Mango 2 4C + 12C |
| Mango | 4C + 8C | 3 | 4.3 | 12250 | 3 | pool | 11500 | 4.088136 | 4.060698 | Mango 3 4C + 8C |
| Mango | 4C + 12C | 3 | 4.3 | 11500 | 3 | pool | 13000 | 4.060698 | 4.113943 | Mango 3 4C + 12C |
| Mango | 4C + 8C | 4 | 3.6 | 9250 | 1 | pool | 14250 | 3.966142 | 4.153815 | Mango 1 4C + 8C |
| Mango | 4C + 12C | 4 | 3.6 | 9350 | 1 | pool | 945000 | 3.970812 | 5.975432 | Mango 1 4C + 12C |
| Mango | 4C + 8C | 4 | 3.8 | 10250 | 2 | pool | 15750 | 4.010724 | 4.197281 | Mango 2 4C + 8C |
| Mango | 4C + 12C | 4 | 3.8 | 8100 | 2 | pool | 192500 | 3.908485 | 5.284431 | Mango 2 4C + 12C |
| Mango | 4C + 8C | 4 | 4.3 | 13250 | 3 | pool | 17000 | 4.122216 | 4.230449 | Mango 3 4C + 8C |
| Mango | 4C + 12C | 4 | 4.3 | 12750 | 3 | pool | 260000 | 4.105510 | 5.414973 | Mango 3 4C + 12C |
| Mango | 4C + 8C | 5 | 3.6 | 7200 | 1 | pool | 127500 | 3.857333 | 5.105510 | Mango 1 4C + 8C |
| Mango | 4C + 12C | 5 | 3.6 | 7750 | 1 | pool | 43300000 | 3.889302 | 7.636488 | Mango 1 4C + 12C |
| Mango | 4C + 8C | 5 | 3.8 | 6725 | 2 | pool | 960000 | 3.827692 | 5.982271 | Mango 2 4C + 8C |
| Mango | 4C + 12C | 5 | 3.8 | 7425 | 2 | pool | 222500 | 3.870697 | 5.347330 | Mango 2 4C + 12C |
| Mango | 4C + 8C | 5 | 4.3 | 10250 | 3 | pool | 102500 | 4.010724 | 5.010724 | Mango 3 4C + 8C |
| Mango | 4C + 12C | 5 | 4.3 | 8750 | 3 | pool | 2325000 | 3.942008 | 6.366423 | Mango 3 4C + 12C |
| Mango | 4C + 8C | 6 | 3.6 | 10250 | 1 | pool | 450000 | 4.010724 | 5.653213 | Mango 1 4C + 8C |
| Mango | 4C + 12C | 6 | 3.6 | 8000 | 1 | pool | 98750000 | 3.903090 | 7.994537 | Mango 1 4C + 12C |
| Mango | 4C + 8C | 6 | 3.8 | 7000 | 2 | pool | 1050000 | 3.845098 | 6.021189 | Mango 2 4C + 8C |
| Mango | 4C + 12C | 6 | 3.8 | 7625 | 2 | pool | 2675000 | 3.882240 | 6.427324 | Mango 2 4C + 12C |
| Mango | 4C + 8C | 6 | 4.3 | 11250 | 3 | pool | 300000 | 4.051152 | 5.477121 | Mango 3 4C + 8C |
| Mango | 4C + 12C | 6 | 4.3 | 9000 | 3 | pool | 2175000 | 3.954242 | 6.337459 | Mango 3 4C + 12C |
| Cantaloupe | 4C + 8C | 0 | 5.6 | 10850 | 1 | pool | 17750 | 4.035430 | 4.249198 | Cantaloupe 1 4C + 8C |
| Cantaloupe | 4C + 12C | 0 | 5.6 | 10850 | 1 | pool | 17750 | 4.035430 | 4.249198 | Cantaloupe 1 4C + 12C |
| Cantaloupe | 4C + 8C | 0 | 5.7 | 8900 | 2 | pool | 11500 | 3.949390 | 4.060698 | Cantaloupe 2 4C + 8C |
| Cantaloupe | 4C + 12C | 0 | 5.7 | 8900 | 2 | pool | 11500 | 3.949390 | 4.060698 | Cantaloupe 2 4C + 12C |
| Cantaloupe | 4C + 8C | 0 | 6.4 | 10575 | 3 | pool | 24500 | 4.024280 | 4.389166 | Cantaloupe 3 4C + 8C |
| Cantaloupe | 4C + 12C | 0 | 6.4 | 10575 | 3 | pool | 24500 | 4.024280 | 4.389166 | Cantaloupe 3 4C + 12C |
| Cantaloupe | 4C + 8C | 3 | 5.6 | 185000 | 1 | pool | 350000 | 5.267172 | 5.544068 | Cantaloupe 1 4C + 8C |
| Cantaloupe | 4C + 12C | 3 | 5.6 | 172500 | 1 | pool | 775000 | 5.236789 | 5.889302 | Cantaloupe 1 4C + 12C |
| Cantaloupe | 4C + 8C | 3 | 5.7 | 102500 | 2 | pool | 122500 | 5.010724 | 5.088136 | Cantaloupe 2 4C + 8C |
| Cantaloupe | 4C + 12C | 3 | 5.7 | 175000 | 2 | pool | 660000 | 5.243038 | 5.819544 | Cantaloupe 2 4C + 12C |
| Cantaloupe | 4C + 8C | 3 | 6.4 | 150000 | 3 | pool | 475000 | 5.176091 | 5.676694 | Cantaloupe 3 4C + 8C |
| Cantaloupe | 4C + 12C | 3 | 6.4 | 190000 | 3 | pool | 477500 | 5.278754 | 5.678973 | Cantaloupe 3 4C + 12C |
| Cantaloupe | 4C + 8C | 4 | 5.6 | 1182500 | 1 | pool | 3775000 | 6.072801 | 6.576917 | Cantaloupe 1 4C + 8C |
| Cantaloupe | 4C + 12C | 4 | 5.6 | 4102500 | 1 | pool | 74000000 | 6.613049 | 7.869232 | Cantaloupe 1 4C + 12C |
| Cantaloupe | 4C + 8C | 4 | 5.7 | 665000 | 2 | pool | 2350000 | 5.822822 | 6.371068 | Cantaloupe 2 4C + 8C |
| Cantaloupe | 4C + 12C | 4 | 5.7 | 375000 | 2 | pool | 2625000 | 5.574031 | 6.419129 | Cantaloupe 2 4C + 12C |
| Cantaloupe | 4C + 8C | 4 | 6.4 | 967500 | 3 | pool | 5800000 | 5.985651 | 6.763428 | Cantaloupe 3 4C + 8C |
| Cantaloupe | 4C + 12C | 4 | 6.4 | 5675000 | 3 | pool | 156750000 | 6.753966 | 8.195208 | Cantaloupe 3 4C + 12C |
| Cantaloupe | 4C + 8C | 5 | 5.6 | 2875000 | 1 | pool | 20250000 | 6.458638 | 7.306425 | Cantaloupe 1 4C + 8C |
| Cantaloupe | 4C + 12C | 5 | 5.6 | 2650000 | 1 | pool | 180000000 | 6.423246 | 8.255273 | Cantaloupe 1 4C + 12C |
| Cantaloupe | 4C + 8C | 5 | 5.7 | 1025000 | 2 | pool | 2100000 | 6.010724 | 6.322219 | Cantaloupe 2 4C + 8C |
| Cantaloupe | 4C + 12C | 5 | 5.7 | 1625000 | 2 | pool | 31000000 | 6.210853 | 7.491362 | Cantaloupe 2 4C + 12C |
| Cantaloupe | 4C + 8C | 5 | 6.4 | 4675000 | 3 | pool | 36500000 | 6.669782 | 7.562293 | Cantaloupe 3 4C + 8C |
| Cantaloupe | 4C + 12C | 5 | 6.4 | 6575000 | 3 | pool | 750000000 | 6.817896 | 8.875061 | Cantaloupe 3 4C + 12C |
| Cantaloupe | 4C + 8C | 6 | 5.6 | 1525000 | 1 | pool | 28500000 | 6.183270 | 7.454845 | Cantaloupe 1 4C + 8C |
| Cantaloupe | 4C + 12C | 6 | 5.6 | 2275000 | 1 | pool | 635000000 | 6.356981 | 8.802774 | Cantaloupe 1 4C + 12C |
| Cantaloupe | 4C + 8C | 6 | 5.7 | 270000 | 2 | pool | 420000 | 5.431364 | 5.623249 | Cantaloupe 2 4C + 8C |
| Cantaloupe | 4C + 12C | 6 | 5.7 | 1300000 | 2 | pool | 950000 | 6.113943 | 5.977724 | Cantaloupe 2 4C + 12C |
| Cantaloupe | 4C + 8C | 6 | 6.4 | 3800000 | 3 | pool | 157500000 | 6.579784 | 8.197281 | Cantaloupe 3 4C + 8C |
| Cantaloupe | 4C + 12C | 6 | 6.4 | 4250000 | 3 | pool | 765000000 | 6.628389 | 8.883661 | Cantaloupe 3 4C + 12C |
Modelling
Make a Listeria model
model the effect of salad, temperature and pH on the change in logLM over time
#make a model
m_gp <- lm(gp ~ pH + fruit+temp.+ t,data=data.1)
#MODEL CHECKS
# Check normality of the residuals
hist(resid(m_gp))
qqnorm(resid(m_gp))
qqline(resid(m_gp))
# Check constant variance of the residuals
plot(m_gp)
# Model summary with effect estimates
summary(m_gp)##
## Call:
## lm(formula = gp ~ pH + fruit + temp. + t, data = data.1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.59749 -0.35618 -0.02739 0.32525 1.73445
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.85471 0.71356 -5.402 1.66e-06 ***
## pH 0.86474 0.14716 5.876 3.02e-07 ***
## fruitCoconut -0.08216 0.36760 -0.224 0.824
## fruitFruit mix 1 0.19575 0.31008 0.631 0.531
## fruitFruit mix 2 -0.06251 0.26159 -0.239 0.812
## fruitFruit mix 3 -0.13365 0.27491 -0.486 0.629
## fruitMango NA NA NA NA
## temp.4 C - 8 C -0.15653 0.16992 -0.921 0.361
## t 0.24431 0.04126 5.921 2.56e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6581 on 52 degrees of freedom
## Multiple R-squared: 0.7456, Adjusted R-squared: 0.7114
## F-statistic: 21.78 on 7 and 52 DF, p-value: 2.103e-13anova(m_gp)## Analysis of Variance Table
##
## Response: gp
## Df Sum Sq Mean Sq F value Pr(>F)
## pH 1 49.913 49.913 115.2435 8.476e-15 ***
## fruit 4 0.556 0.139 0.3210 0.8626
## temp. 1 0.368 0.368 0.8486 0.3612
## t 1 15.185 15.185 35.0603 2.564e-07 ***
## Residuals 52 22.522 0.433
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1This looks reasonable, and fits the data better than linear mixed effects models that we tried.
model the total viable counts
m_PC <- lmer(logPC ~ factor(t)+pH.average+product+temp+
(1|salad_rep), data=data.2)
m_PC <- lm(logPC ~ factor(t)+pH.average+product+temp, data=data.2)
#MODEL CHECKS
# Check normality of the residuals
hist(resid(m_PC))
qqnorm(resid(m_PC))
qqline(resid(m_PC))
# Check constant variance of the residuals
plot(m_PC)
# Model summary with effect estimates
summary(m_PC)##
## Call:
## lm(formula = logPC ~ factor(t) + pH.average + product + temp,
## data = data.2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.88708 -0.40608 0.06774 0.47427 1.50460
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.2627 1.5547 2.742 0.00677 **
## factor(t)3 0.5162 0.1716 3.009 0.00303 **
## factor(t)4 1.6214 0.1716 9.451 < 2e-16 ***
## factor(t)5 2.3629 0.1716 13.772 < 2e-16 ***
## factor(t)6 2.6771 0.1716 15.604 < 2e-16 ***
## pH.average 0.1623 0.2617 0.620 0.53609
## productCoconut 0.3763 0.2290 1.643 0.10221
## productFruit mix 1 -1.0848 0.6808 -1.593 0.11294
## productFruit mix 2 -0.8675 0.5398 -1.607 0.10993
## productFruit mix 3 -1.2168 0.5480 -2.220 0.02772 *
## productMango -1.0341 0.5562 -1.859 0.06476 .
## temp4C + 8C -0.5086 0.1085 -4.688 5.69e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7279 on 168 degrees of freedom
## Multiple R-squared: 0.7795, Adjusted R-squared: 0.765
## F-statistic: 53.98 on 11 and 168 DF, p-value: < 2.2e-16anova(m_PC)## Analysis of Variance Table
##
## Response: logPC
## Df Sum Sq Mean Sq F value Pr(>F)
## factor(t) 4 192.305 48.076 90.7415 < 2.2e-16 ***
## pH.average 1 105.524 105.524 199.1702 < 2.2e-16 ***
## product 5 5.119 1.024 1.9323 0.09149 .
## temp 1 11.642 11.642 21.9744 5.687e-06 ***
## Residuals 168 89.009 0.530
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot the data
#SETUP-------------------------------------------------------------------------
#make a title which is partially in italics because I don't know how to do this in ggtitle
LM_title <- expression(paste("Model for ", italic("Listeria monocytogenes"), " on fruit products"))
LM_title2 <- expression(paste("CFU count of ", italic("Listeria monocytogenes"), " on fruit products"))
#calculate means, SD, SE of the data.
data.2 %>%
group_by(product,temp,t) %>%
summarize(N=length(LM),
lmean = mean(logLM),
lsd = sd(logLM),
lse = sd(logLM) / sqrt(length(logLM)),
lmeanPC = mean(logPC),
lsdPC = sd(logPC),
lsePC = sd(logPC) / sqrt(length(logPC))) %>%
mutate(mean=10^lmean,
mean_plus_sd = 10^(lmean + lsd),
mean_minus_sd = 10^(lmean - lsd),
meanPC = 10^(lmeanPC),
meanPC_plus_sd = 10^(lmeanPC + lsdPC),
meanPC_minus_sd = 10^(lmeanPC - lsdPC)) -> cdata## Warning: package 'bindrcpp' was built under R version 3.4.4#do the Listeria CFU/g plot:
ggplot(cdata, aes(x=t, y=mean, color = product))+
labs(title = LM_title2,
subtitle="Starting concentration: 10^4 CFU/g",
caption="Ribbon: SD",
x="Time (days)",
y="mean log CFU/g",
linetype="product",
shape="product",
color="product",
fill="product") +
geom_point() +
geom_text(aes(label= round(log10(mean), digits = 1), vjust=-0.6)) +
geom_ribbon(group=1, aes(ymin=mean_minus_sd,
ymax=mean_plus_sd,
fill=product,
linetype=NA), alpha=0.2) +
geom_line(group=1) +
scale_y_log10(limits=c(2000, 5000000000))+
#ylim(1, 11000000)+
facet_grid(product~temp)
#plot total viable count CFU/g
ggplot(cdata, aes(x=t, y=meanPC, color = product))+
labs(title= "Mean CFU for the TVC (total viable count) in the inoculated samples",
caption="Ribbon: SD",
x="Time (days)",
y="mean log CFU/g",
linetype="product",
shape="product",
color="product",
fill="product") +
geom_point() +
geom_text(aes(label= round(log10(meanPC), digits = 1), vjust=-0.6)) +
geom_ribbon(group=1, aes(ymin=meanPC_minus_sd,
ymax=meanPC_plus_sd,
fill=product,
linetype=NA), alpha=0.2) +
geom_line(group=1) +
scale_y_log10(limits=c(1, 100000000000))+
facet_grid(product~temp)
#
#