Cortisol Concentration Values, Test4
Paloma Contreras
2025-04-03
Last updated: 2025-04-03
Checks: 6 1
Knit directory:
HairCort-Evaluation-Nist2020/
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Summary
Cortisol value calculations
| Min. | 1st Qu. | Median | Mean | 3rd Qu. | Max. | NA’s | |
|---|---|---|---|---|---|---|---|
| A) Standard Method | 0.4142 | 1.9653 | 7.5533 | 14.1906 | 28.0667 | 50.933 | 3 |
| B) Spike-Corrected Method | -45.870 | -31.922 | -1.929 | -9.444 | 7.553 | 30.780 | 3 |
| C) Standard, but simplified equation | 0.4142 | 1.9653 | 7.5533 | 14.1906 | 28.0667 | 50.9333 | 3 |
| D) Spike-Corrected (divided by two) | -11.167 | -4.193 | 2.349 | 5.314 | 17.368 | 30.780 | 3 |
Results:
Intra-assay CV: 14.5%
Intra-assay CV after removing low quality samples: 10%
Inter-assay CV: 21%
(Bindings for 20mg sample diluted in 250 uL, no spike: 64.8% and 48% in test3 and test4, respectively)
Conclusions:
Concerns: Overall quality of the plate is not great, but serial dilusions show clear parallelism and standards have values within the expected
Cortisol concentration calculations
# define volume of methanol used for cortisol extraction
# vol added / vol recovered (mL)
extraction <- 1/0.750
# set reading value of spike (std1, 0.333 ug/dL),
# and transforming to ug.dL
std <- (3191+3228)/2
std.r <- (std/10000)
std.r[1] 0.32095# according to chatgpt, the spike's contribution is
# 1600 pg/mL, which is very similar to half of the reading for std 1 :]Loading files and transforming units, including low quality data
df <- read.csv(file.path(data_path,"Data_QC_flagged.csv"))
kable(tail(df))| Wells | Sample | Category | Weight_mg | Buffer_nl | Spike | SpikeVol_uL | Dilution | Raw.OD | Binding.Perc | Conc_pg.ml | Ave_Conc_pg.ml | CV.Perc | SD | SEM | CV_categ | Binding.Perc_categ | Failed_samples | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 77 | G11 | TP3A | P | 12 | 220 | 1 | 25 | 1 | 0.258 | 23.2 | 2800 | 2792 | 0.391 | 10.9 | 7.71 | NA | NA | NA |
| 78 | H11 | TP3A | P | 12 | 220 | 1 | 25 | 1 | 0.259 | NA | 2785 | NA | NA | NA | NA | NA | NA | NA |
| 79 | A12 | TP3B | P | 12 | 60 | 1 | 25 | 1 | 0.195 | 15.5 | 4084 | 4210 | 4.230 | 178.0 | 126.00 | NA | UNDER 20% binding | UNDER 20% binding |
| 80 | B12 | TP3B | P | 12 | 60 | 1 | 25 | 1 | 0.186 | NA | 4336 | NA | NA | NA | NA | NA | NA | NA |
| 81 | C12 | TP3C | P | 12 | 60 | 1 | 25 | 1 | 0.186 | 13.9 | 4336 | 4661 | 9.870 | 460.0 | 325.00 | NA | UNDER 20% binding | UNDER 20% binding |
| 82 | D12 | TP3C | P | 12 | 60 | 1 | 25 | 1 | 0.166 | NA | 4986 | NA | NA | NA | NA | NA | NA | NA |
# remove outlier
df<- df[(df$Sample != "TP3A"),]
# Creating variables in indicated units
# dilution (buffer)
df$Buffer_ml <- c(df$Buffer_nl/1000)
# remove unnecessary information
data <- df %>%
dplyr::select(Wells, Sample, Category, Binding.Perc, Ave_Conc_pg.ml, Weight_mg, Buffer_ml, Spike, SpikeVol_uL, Dilution, Failed_samples)
kable(tail(data, 10))| Wells | Sample | Category | Binding.Perc | Ave_Conc_pg.ml | Weight_mg | Buffer_ml | Spike | SpikeVol_uL | Dilution | Failed_samples | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 71 | A11 | TP2A | P | 17.3 | 3793 | 9 | 0.06 | 1 | 25 | 1 | UNDER 20% binding |
| 72 | B11 | TP2A | P | NA | NA | 9 | 0.06 | 1 | 25 | 1 | NA |
| 73 | C11 | TP2B | P | 21.1 | 3101 | 9 | 0.06 | 1 | 25 | 1 | NA |
| 74 | D11 | TP2B | P | NA | NA | 9 | 0.06 | 1 | 25 | 1 | NA |
| 75 | E11 | TP2C | P | 18.1 | 3634 | 9 | 0.06 | 1 | 25 | 1 | UNDER 20% binding |
| 76 | F11 | TP2C | P | NA | NA | 9 | 0.06 | 1 | 25 | 1 | NA |
| 79 | A12 | TP3B | P | 15.5 | 4210 | 12 | 0.06 | 1 | 25 | 1 | UNDER 20% binding |
| 80 | B12 | TP3B | P | NA | NA | 12 | 0.06 | 1 | 25 | 1 | NA |
| 81 | C12 | TP3C | P | 13.9 | 4661 | 12 | 0.06 | 1 | 25 | 1 | UNDER 20% binding |
| 82 | D12 | TP3C | P | NA | NA | 12 | 0.06 | 1 | 25 | 1 | NA |
dim(data)[1] 80 11# remove duplicates
data <- data[!is.na(data$Binding.Perc), ](A) Standard Calculation
Formula:
((A/B) * (C/D) * E * 10,000) = F
- A = μg/dl from assay output;
- B = weight (in mg) of hair subjected to extraction;
- C = vol. (in ml) of methanol added to the powdered hair;
- D = vol. (in ml) of methanol recovered from the extract and subsequently dried down;
- E = vol. (in ml) of assay buffer used to reconstitute the dried extract;
- F = final value of hair CORT Concentration in pg/mg.
##################################
##### Calculate final values #####
##################################
# Transform to μg/dl from assay output
data$Ave_Conc_ug.dL <- c(data$Ave_Conc_pg.ml/10000)
data$Final_conc_pg.mg <- c(
(data$Ave_Conc_ug.dL / data$Weight_mg) * # A/B *
extraction * # C/D *
data$Buffer_ml * 10000) # E * 10000
data <- data[order(data$Sample),]
write.csv(data, file.path(data_path, "Data_cort_values_methodA.csv"), row.names = F)
# summary for all samples
summary(data$Final_conc_pg.mg) Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
0.4142 1.9653 7.5533 14.1906 28.0667 50.9333 3 kable(tail(data, 7))| Wells | Sample | Category | Binding.Perc | Ave_Conc_pg.ml | Weight_mg | Buffer_ml | Spike | SpikeVol_uL | Dilution | Failed_samples | Ave_Conc_ug.dL | Final_conc_pg.mg | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 67 | E10 | TP1B | P | 18.1 | 3820 | 6 | 0.06 | 1 | 25 | 1 | HIGH CV;UNDER 20% binding | 0.3820 | 50.93333 |
| 69 | G10 | TP1C | P | 27.8 | 2242 | 6 | 0.06 | 1 | 25 | 1 | NA | 0.2242 | 29.89333 |
| 71 | A11 | TP2A | P | 17.3 | 3793 | 9 | 0.06 | 1 | 25 | 1 | UNDER 20% binding | 0.3793 | 33.71556 |
| 73 | C11 | TP2B | P | 21.1 | 3101 | 9 | 0.06 | 1 | 25 | 1 | NA | 0.3101 | 27.56444 |
| 75 | E11 | TP2C | P | 18.1 | 3634 | 9 | 0.06 | 1 | 25 | 1 | UNDER 20% binding | 0.3634 | 32.30222 |
| 79 | A12 | TP3B | P | 15.5 | 4210 | 12 | 0.06 | 1 | 25 | 1 | UNDER 20% binding | 0.4210 | 28.06667 |
| 81 | C12 | TP3C | P | 13.9 | 4661 | 12 | 0.06 | 1 | 25 | 1 | UNDER 20% binding | 0.4661 | 31.07333 |
dim(data)[1] 40 13(B) Accounting for Spike
We followed the procedure described in Nist et al. 2020:
“Thus, after pipetting 25μL of standards and samples into the appropriate wells of the 96-well assay plate, we added 25μL of the 0.333ug/dL standard to all samples, resulting in a 1:2 dilution of samples. The remainder of the manufacturer’s protocol was unchanged. We analyzed the assay plate in a Powerwave plate reader (BioTek, Winooski, VT) at 450nm and subtracted background values from all assay wells. In the calculations, we subtracted the 0.333ug/dL standard reading from the sample readings. Samples that resulted in a negative number were considered nondetectable. We converted cortisol levels from ug/dL, as measured by the assay, to pg/mg—based on the mass of hair collected and analyzed using the following formula:
A/B * C/D * E * 10,000 * 2 = F
where - A = μg/dl from assay output; - B = weight (in mg) of collected hair; - C = vol. (in ml) of methanol added to the powdered hair; - D = vol. (in ml) of methanol recovered from the extract and subsequently dried down; - E = vol. (in ml) of assay buffer used to reconstitute the dried extract; 10,000 accounts for changes in metrics; 2 accounts for the dilution factor after addition of the spike; and - F = final value of hair cortisol concentration in pg/mg”
dSpike <- data
##################################
##### Calculate final values #####
##################################
dSpike$Final_conc_pg.mg <-
ifelse(
dSpike$Spike == 1, ## Only spiked samples
((dSpike$Ave_Conc_ug.dL - std.r) / # (A-spike) / B
dSpike$Weight_mg)
* extraction * # C / D
dSpike$Buffer_ml * 10000 * 2 , # E * 10000 *2
dSpike$Final_conc_pg.mg
)
write.csv(dSpike, file.path(data_path, "Data_cort_values_methodB.csv"), row.names = F)
# summary for all samples
summary(dSpike$Final_conc_pg.mg) Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
-45.870 -31.922 -1.929 -9.444 7.553 30.780 3 dSpikeSub <- data[c(data$Spike == 0), ]
summary(dSpikeSub$Final_conc_pg.mg) Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
0.4142 0.8400 2.3493 7.7984 11.9733 30.7800 3 kable(tail(dSpike, 10))| Wells | Sample | Category | Binding.Perc | Ave_Conc_pg.ml | Weight_mg | Buffer_ml | Spike | SpikeVol_uL | Dilution | Failed_samples | Ave_Conc_ug.dL | Final_conc_pg.mg | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 61 | G9 | TD6 | D | 99.7 | 81.99 | 20 | 0.11 | 1 | 0 | 0.031250 | ABOVE 80% binding | 0.008199 | -45.870147 |
| 63 | A10 | TD7 | D | 99.0 | 86.73 | 20 | 0.11 | 1 | 0 | 0.015625 | ABOVE 80% binding | 0.008673 | -45.800627 |
| 65 | C10 | TP1A | P | 21.8 | 2986.00 | 6 | 0.06 | 1 | 25 | 1.000000 | NA | 0.298600 | -5.960000 |
| 67 | E10 | TP1B | P | 18.1 | 3820.00 | 6 | 0.06 | 1 | 25 | 1.000000 | HIGH CV;UNDER 20% binding | 0.382000 | 16.280000 |
| 69 | G10 | TP1C | P | 27.8 | 2242.00 | 6 | 0.06 | 1 | 25 | 1.000000 | NA | 0.224200 | -25.800000 |
| 71 | A11 | TP2A | P | 17.3 | 3793.00 | 9 | 0.06 | 1 | 25 | 1.000000 | UNDER 20% binding | 0.379300 | 10.373333 |
| 73 | C11 | TP2B | P | 21.1 | 3101.00 | 9 | 0.06 | 1 | 25 | 1.000000 | NA | 0.310100 | -1.928889 |
| 75 | E11 | TP2C | P | 18.1 | 3634.00 | 9 | 0.06 | 1 | 25 | 1.000000 | UNDER 20% binding | 0.363400 | 7.546667 |
| 79 | A12 | TP3B | P | 15.5 | 4210.00 | 12 | 0.06 | 1 | 25 | 1.000000 | UNDER 20% binding | 0.421000 | 13.340000 |
| 81 | C12 | TP3C | P | 13.9 | 4661.00 | 12 | 0.06 | 1 | 25 | 1.000000 | UNDER 20% binding | 0.466100 | 19.353333 |
(C) Skip unit transformation
##################################
##### Calculate final values #####
##################################
data$Final_conc_pg.mg <- c(
(data$Ave_Conc_pg.ml / data$Weight_mg) * # A/B *
extraction * # C/D *
data$Buffer_ml) # E
datac <- data[order(data$Sample),]
write.csv(datac, file.path(data_path, "Data_cort_values_methodC.csv"), row.names = F)
# summary for all samples
summary(datac$Final_conc_pg.mg) Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
0.4142 1.9653 7.5533 14.1906 28.0667 50.9333 3 (D) Account for Spike (contribution / 2)
Spike contribution (pg/mL) = (Vol. spike (mL) x Conc. spike (pg) ) / Vol. reconstitution (mL)
# Calculate contribution of spike according to the different volumes in which it was added
# considere that contribution in serial dilutions is smaller
#datac$Spike.cont_pg.mL <- datac
##################################
##### Calculate final values #####
##################################
dSpiked <- datac
dSpiked$Final_conc_pg.mg <-
ifelse(
dSpike$Spike == 1, ## Only spiked samples
((dSpike$Ave_Conc_pg.ml - (std/2)) / # (A-(spike/2)) / B
dSpike$Weight_mg)
* extraction * # C / D
dSpike$Buffer_ml, # E *
dSpike$Final_conc_pg.mg
)
write.csv(dSpiked, file.path(data_path, "Data_cort_values_methodD.csv"), row.names = F)
# summary for all samples
summary(dSpiked$Final_conc_pg.mg) Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
-11.167 -4.193 2.349 5.314 17.368 30.780 3 Plots
(A) Standard Calculation
# scatterplot method A
data$Spike <- replace(data$Spike, data$Spike == 1, 'Yes')
data$Spike <- replace(data$Spike, data$Spike == 0, 'No')
data$Buffer <- data$Buffer_ml
data$Buffer <- replace(data$Buffer, data$Buffer == 0.06, '60 uL')
data$Buffer <- replace(data$Buffer, data$Buffer == 0.11, '110 uL')
data$Buffer <- replace(data$Buffer, data$Buffer == 0.25, '250 uL')
ggplot(data, aes(y = Final_conc_pg.mg,
x = Weight_mg,
color = Spike,
shape = Buffer)) +
geom_point(size = 2.5, alpha = 0.85) +
geom_text(aes(label = Sample), size = 2.5, vjust = -0.65, hjust = -0.18) +
theme_minimal() +
geom_hline(yintercept = 0,
linetype = "dashed", color = "red") +
xlim(0,52) +
labs(
title = "(A) Standard Calculation Cortisol Values",
y = "Final Concentration (pg/mg)",
x = "Weight (mg)") +
theme(
plot.title = element_text(hjust = 0.5,
size = 17, face = "bold"),
axis.title = element_text(size = 14),
axis.text = element_text(size = 12)
) +
scale_color_paletteer_d("vangogh::CafeTerrace")Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_text()`).
(B) Accounting for Spike
dSpike$Spike <- replace(dSpike$Spike, dSpike$Spike == 1, 'Yes')
dSpike$Spike <- replace(dSpike$Spike, dSpike$Spike == 0, 'No')
dSpike$Buffer <- dSpike$Buffer_ml
dSpike$Buffer <- replace(dSpike$Buffer, dSpike$Buffer == 0.06, '60 uL')
dSpike$Buffer <- replace(dSpike$Buffer, dSpike$Buffer == 0.11, '110 uL')
dSpike$Buffer <- replace(dSpike$Buffer, dSpike$Buffer == 0.25, '250 uL')
# scatterplot
ggplot(dSpike, aes(y = Final_conc_pg.mg,
x = Weight_mg,
color = Spike,
shape = Buffer)) +
geom_point(size = 3.5, alpha = 0.85) +
geom_text(aes(label = Sample), size = 3, vjust = -1, hjust = -0.1) +
theme_minimal() +
xlim(0,52) +
geom_hline(yintercept = 0,
linetype = "dashed", color = "red") +
labs(
title = "(B) Calculation Accounting for Spike",
y = "Final Concentration (pg/mg)",
x = "Weight (mg)" ) +
theme(
plot.title = element_text(hjust = 0.5,
size = 17, face = "bold"),
axis.title = element_text(size = 14),
axis.text = element_text(size = 12)
)+
scale_color_paletteer_d("vangogh::CafeTerrace")Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_text()`).
(C)
# scatterplot method c
datac$Spike <- replace(datac$Spike, data$Spike == 1, 'Yes')
datac$Spike <- replace(datac$Spike, data$Spike == 0, 'No')
datac$Buffer <- data$Buffer_ml
datac$Buffer <- replace(datac$Buffer, data$Buffer == 0.06, '60 uL')
datac$Buffer <- replace(datac$Buffer, data$Buffer == 0.11, '110 uL')
datac$Buffer <- replace(datac$Buffer, data$Buffer == 0.25, '250 uL')
ggplot(datac, aes(y = Final_conc_pg.mg,
x = Weight_mg,
color = Spike,
shape = Buffer)) +
geom_point(size = 2.5, alpha = 0.85) +
geom_text(aes(label = Sample), size = 2.5, vjust = -0.65, hjust = -0.18) +
theme_minimal() +
geom_hline(yintercept = 0,
linetype = "dashed", color = "red") +
#ylim(-26,24) +
# xlim(0,52) +
labs(
title = "(C) ",
y = "Final Concentration (pg/mg)",
x = "Weight (mg)") +
theme(
plot.title = element_text(hjust = 0.5,
size = 17, face = "bold"),
axis.title = element_text(size = 14),
axis.text = element_text(size = 12)
) +
scale_color_paletteer_d("vangogh::CafeTerrace")Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_text()`).
D
dSpiked$Spike <- replace(dSpiked$Spike, dSpiked$Spike == 1, 'Yes')
dSpiked$Spike <- replace(dSpiked$Spike, dSpiked$Spike == 0, 'No')
dSpiked$Buffer <- dSpiked$Buffer_ml
dSpiked$Buffer <- replace(dSpiked$Buffer, dSpiked$Buffer == 0.06, '60 uL')
dSpiked$Buffer <- replace(dSpiked$Buffer, dSpiked$Buffer == 0.11, '110 uL')
dSpiked$Buffer <- replace(dSpiked$Buffer, dSpiked$Buffer == 0.25, '250 uL')
# scatterplot
ggplot(dSpiked, aes(y = Final_conc_pg.mg,
x = Weight_mg,
color = Spike,
shape = Buffer)) +
geom_point(size = 3.5, alpha = 0.85) +
geom_text(aes(label = Sample), size = 3, vjust = -1, hjust = -0.1) +
theme_minimal() +
ylim(-26,30) +
xlim(0,52) +
geom_hline(yintercept = 0,
linetype = "dashed", color = "red") +
labs(
title = "(D) ",
y = "Final Concentration (pg/mg)",
x = "Weight (mg)" ) +
theme(
plot.title = element_text(hjust = 0.5,
size = 17, face = "bold"),
axis.title = element_text(size = 14),
axis.text = element_text(size = 12)
)+
scale_color_paletteer_d("vangogh::CafeTerrace")Warning: Removed 4 rows containing missing values or values outside the scale range
(`geom_point()`).Warning: Removed 4 rows containing missing values or values outside the scale range
(`geom_text()`).
Evaluation
# non-spiked samples only
data2 <-data
#two datasets, separated by dilution
data2.06 <- data2[data2$Buffer == "60 uL", ]
data2.11 <- data2[data2$Buffer == "110 uL", ]
data2.25 <- data2[data2$Buffer == "250 uL", ]
#### fit models ####
# model Buffer = 0.06
model06 <- lm(Final_conc_pg.mg ~ Weight_mg,
data = data2.06)
r_squared06 <- summary(model06)$r.squared
# model Buffer = 0.25
model25 <- lm(Final_conc_pg.mg ~ Weight_mg,
data = data2.25)
r_squared25 <- summary(model25)$r.squared
# Calculate residuals
residuals06 <- residuals(model06)
residuals25 <- residuals(model25)
# Quantify residuals
# Mean Absolute Error
mae06 <- mean(abs(residuals06))
# Standard Deviation of Residuals
std_dev06 <- sd(residuals06)
# Mean Absolute Error
mae25 <- mean(abs(residuals25))
# Standard Deviation of Residuals
std_dev25 <- sd(residuals25)
# scatterplot
ggplot(data2, aes(y = Final_conc_pg.mg,
x = Weight_mg,
color = Category,
fill = Category)) +
geom_point(size = 2.5) +
geom_text(label = c(data2$Sample), nudge_y = 0.75, nudge_x = -0.5) +
geom_smooth(method = "lm",
color = "gold3",
se = TRUE,
alpha = 0.1) +
geom_hline(yintercept = mean(data2$Final_conc_pg.mg),
color = "gray80",
linetype = "dashed") +
geom_hline(yintercept = mean(data2.06$Final_conc_pg.mg),
color = "lightblue3",
linetype = "dashed") +
geom_hline(yintercept = mean(data2.25$Final_conc_pg.mg),
color = "lightpink3",
linetype = "dashed") +
theme_minimal() +
xlim(5, max(data2$Weight_mg) + 4) +
ylim(0, max(data2$Final_conc_pg.mg)+4) +
labs(
title = "Final Cort Concentration and Weight
(Non-spiked only)",
y = "Final Concentration (pg/mg)",
x = "Weight (mg)"
) +
theme(
plot.title = element_text(hjust = 0.5, size = 16, face = "bold"),
axis.title = element_text(size = 14),
axis.text = element_text(size = 12)
) +
# Add R^2 annotation
annotate("text", x = max(data2$Weight_mg) * 0.7,
y = min(data2$Final_conc_pg.mg) * 1.5,
label = paste("R² =", round(r_squared06, 3)),
size = 5, color = "black") +
annotate("text", x = max(data2$Weight_mg) * 0.7,
y = max(data2$Final_conc_pg.mg) * 0.84,
label = paste("R² =", round(r_squared25, 3)),
size = 5, color = "black")Warning: Removed 3 rows containing non-finite outside the scale range
(`stat_smooth()`).Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_text()`).Warning: Removed 1 row containing missing values or values outside the scale range
(`geom_hline()`).
Removed 1 row containing missing values or values outside the scale range
(`geom_hline()`).
Removed 1 row containing missing values or values outside the scale range
(`geom_hline()`).Warning: Removed 1 row containing missing values or values outside the scale range
(`geom_text()`).
Removed 1 row containing missing values or values outside the scale range
(`geom_text()`).
The previous figure shows that:
- results are very stable across weights, particularly for the samples where a dilution of 250 uL was used
- there is more error when using a dilution of 60 uL
- dilution affects estimation of cortisol concentration in a significant way: even though final concentration numbers account for differences in the dilutions, the results we observe for each group do not overlap
- the average value when using 250 uL of buffer is twice as big as when using 60 uL
Optimal dilution
Error using 0.06 mL buffer
Mean Absolute Error (MAE) 0.06 mL: 4.064 Standard Deviation of Residuals 0.06 mL: 6.235 Error using 0.25 mL buffer
Mean Absolute Error (MAE) 0.25 mL: 7.328 Standard Deviation of Residuals 0.25 mL: 9.695 From this we conclude that using a 250 uL dilution provides more consistent results
sessionInfo()R version 4.4.3 (2025-02-28)
Platform: aarch64-apple-darwin20
Running under: macOS Sequoia 15.3.2
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/Detroit
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] dplyr_1.1.4 paletteer_1.6.0 broom_1.0.7 ggplot2_3.5.1
[5] knitr_1.49
loaded via a namespace (and not attached):
[1] sass_0.4.9 utf8_1.2.4 generics_0.1.3 tidyr_1.3.1
[5] prismatic_1.1.2 lattice_0.22-6 stringi_1.8.4 digest_0.6.37
[9] magrittr_2.0.3 evaluate_1.0.1 grid_4.4.3 fastmap_1.2.0
[13] Matrix_1.7-2 rprojroot_2.0.4 workflowr_1.7.1 jsonlite_1.8.9
[17] backports_1.5.0 rematch2_2.1.2 promises_1.3.0 mgcv_1.9-1
[21] purrr_1.0.2 fansi_1.0.6 scales_1.3.0 jquerylib_0.1.4
[25] cli_3.6.3 rlang_1.1.4 splines_4.4.3 munsell_0.5.1
[29] withr_3.0.2 cachem_1.1.0 yaml_2.3.10 tools_4.4.3
[33] colorspace_2.1-1 httpuv_1.6.15 vctrs_0.6.5 R6_2.5.1
[37] lifecycle_1.0.4 git2r_0.35.0 stringr_1.5.1 fs_1.6.5
[41] pkgconfig_2.0.3 pillar_1.9.0 bslib_0.8.0 later_1.3.2
[45] gtable_0.3.6 glue_1.8.0 Rcpp_1.0.13-1 xfun_0.49
[49] tibble_3.2.1 tidyselect_1.2.1 rstudioapi_0.17.1 farver_2.1.2
[53] nlme_3.1-167 htmltools_0.5.8.1 rmarkdown_2.29 labeling_0.4.3
[57] compiler_4.4.3