PARAFAC analysis of EEM data to separate DOM components in R
Introduction
staRdom is a package for R version 4 (R Development Core Team 2019) to analyse fluorescence and absorbance data of dissolved organic matter (DOM). The important features are:
- separating the components of the EEMs via PARAFAC/CANDECOMP (Murphy et al. 2013; Bro 1997; Helwig 2019).
- validating the model using a split-half analysis, the core consistency, the model fit or visually examining the residuals
- correcting excitation-emission-matrices (Murphy et al. 2013; Massicotte 2019)
- calculating fluorescence peaks and indices (Massicotte 2019)
- autochthonous productivity index / freshness index [BIX; Huguet et al. (2009); Fellman, Hood, and Spencer (2010)]
- classical peaks based on manual peak picking [B, T, A, M, C; Coble (1996)]
- fluorescence index [FI; McKnight et al. (2001)]
- humification index [HIX; Ohno (2002)]
- calculating common absorbance (slope) parameters:
- absorbance at 254 nm [a254; Dobbs, Wise, and Dean (1972)],
- absorbance at 300 nm [a300; Molot et al. (2005)],
- ratio of absorbance at 250 to 365 nm [E2:E3; De Haan and De Boer (1987)],
- ratio of absorbance at 465 to 665 nm [E4:E6; Summers, Cornel, and Roberts (1987)],
- spectral slope within log-transformed absorption spectra range (S275-295, S350-400, S300-700) and the ratio of S275-295 to S350-400 (SR) (Helms et al. 2008),
- the wavelength distribution of absorption spectral slopes (Loiselle et al. 2009) and
- user-defined values and slopes can be extracted or calculated from the absorbance spectra.
staRdom has been developed and is maintained at WasserCluster Lunz (https://www.wcl.ac.at/index.php/en/) and the University of Natural Resources and Life Sciences, Vienna (https://boku.ac.at/).
A comparison in quality of results and performance of the PARAFAC algorithms in staRdom and drEEM can be found in Pucher et al. (2019). The analysis process was developed and discussed in other papers and tutorials (e.g. Murphy et al. 2013). The aim of this package is to provide an elaborate and flexible way of using PARAFAC analysis of EEM data on the R platform. The offered functions follow the concept of Murphy et al. (2013). We strongly recommend to read this paper to understand the underlying procedure of the analysis.
For easy data correction and calculations of peaks, indices and slope parameters in R but without using R functions and codes please see vignette for basic analysis. We use functions from the R package eemR, for information on eemR and its functions please see the eemR vignette. Details on the actual PARAFAC calculation can be found in the multiway documentation.
This tutorial was created using R version 4.4.2 and the packages dplyr (Wickham et al. 2020) and tidyr (Wickham, Henry, and RStudio 2020).
Aim of this document
This document describes a complete fluorescence and absorbance analysis of example data using R functions and offers a variety of options and ways to gain validated results.
Remark on errors and warnings
In R, there can be errors and warnings. Errors stop the calculations and no results are returned because of a severe problem. Warnings do not stop calculations but are hints, that something unusual happened. If you encounter any warnings please think of the reason. In some cases, this reason might be in-line with what you want and is no problem at all. An examples for a not serious warnings are interpolated values because of missing wavelengths or NAs introduced by coercion in some cases. Please have a look at your data to find actual problems.
Install and load staRdom
staRdom can be installed directly from a CRAN repository:
You can also install staRdom from GitHub. The version on GitHub is sometimes a more recent one.
install.packages("devtools") # Run this only, if devtools is not installed already.
devtools::install_github("MatthiasPucher/staRdom")staRdom can then be loaded:
Parallel processing
Some of the functions can use several CPU cores in parallel to speed
up the calculations. You can set the number of parallel processes to be
used. In tests, best results were achieved setting cores to
the number of physical cores in your computer. Using virtual cores
introduced by Hyper-threading did increase calculation times again.
detectCores(logical = FALSE) will give you the appropriate
number. On some computers this function returns the number of virtual
cores, which has to be checked and set manually then.
Overview of analysis steps
The diagram below shows the most important steps in the analysis of fluorescence and absorbance data to identify DOM parameters. After importing the data and applying the desired correction steps, peaks, indices and absorbance parameters can be calculated. Besides that, after the data correction, compounds can be separated using a PARAFAC model. The PARAFAC model development includes cyclical steps to come to a satisfying result. Model validation is very important at that point to get trustful results. As a last step, the compounds determined in the model can be linked to already published ones or other experimental data and by that interpreted in a biogeochemical context.
Example data coming with the package
You can run a complete data correction and analysis as shown in this
example with the data provided by the package and downloaded within the
tutorial. However, you can start the tutorial with your own data right
away. The function system.file() used below returns the
folders, where the example data is stored in. In case you use your own,
you can just type in the path to your data as a string
(e.g. “C:/folder/another folder”) without using
system.file.
Raw EEM data
The example EEM data is saved in a folder and accessible by
system.file("extdata/EEMs", package = "staRdom"). Due to
package size issues, only a small amount of samples is included and for
a complete reproduction of the PARAFAC analysis demonstrated below, the
drEEM data has to be downloaded (see below how to accomplish that).
Raw absorbance data
The absorbance data is saved in a folder accessible by
system.file("extdata/absorbance", package = "staRdom").
Additional raw data
There is a table with data on diluted samples included. The table can
serve as an example in case you worked with diluted samples. It is saved
in a folder accessible by
system.file("extdata/metatable_dreem.csv", package = "staRdom").
Corrected EEM data
The corrected EEM data set is loaded from the drEEM website.
PARAFAC model
An already calculated PARAFAC model was included in the package. It
can be loaded into the R environment by
data(pf_models).
Import raw data
For a complete analysis in staRdom you need fluorescence and absorbance data. In many cases also a metatable is needed. Reading and linking the data needs some preparations and attention. Below we show how to import these data using the provided example data.
EEM data import is done with eem_read (package eemR).
Currently you can use it to import from Varian Cary Eclipse, Horiba
Aqualog, Horiba Fluoromax-4, Shimadzu and Hitachi F-7000 instruments as
well as generic csv files.
folder <- system.file("extdata/EEMs/", package = "staRdom") # folder containing example EEMs
eem_list <- eem_read(folder, recursive = TRUE, import_function = eem_csv) # in case you use your own data, just replace folder by a path. e.g. "C:/folder/another folder" and change import_function according to instrument.This is an example to load data from instrument specific ASCII files.
import_function has to be set accordingly: Varian Cary
Eclipse ("cary"), Horiba Aqualog ("aqualog"),
Horiba Fluoromax-4 ("fluoromax4"), Shimadzu
("shimadzu"), Hitachi F-7000 (eem_hitachi) and
generic csv files (eem_csv when excitation wavelengths are
in columns or eem_csv2 when emission wavelengths are in
columns). Please note, eem_hitachi, eem_csv
and eem_csv2 are without hyphens!
If your instrument is not amongst the mentioned ones, eemR offers the opportunity to create custom import functions (see according vignette).
To have a look at your data, you can plot the samples in several
plots using eem_overview_plot. ggeem is
another function that plots EEMs, but it produces only one plot, which
can be overloaded in case of many samples. spp defines the
number of samples per plot. Not present data is not shown (light
greyish), NAs are dark grey. contour = TRUE adds contour
lines to the EEM plots.
## [[1]]
Absorbance data is imported with absorbance_read. It is
read from CSV or TXT files. absorbance_path is either a
directory and all files in there are read in, or a single file that is
read in. Tables can either contain data from one sample or from several
samples in columns. The first column is considered the wavelength
column. A multi-sample file must have sample names as column names. All
tables are combined to one with one wavelength column and one column for
each sample containing the absorbance data.
absorbance_path = system.file("extdata/absorbance", package = "staRdom") # load example data, set a path without using system.file to use your own data e.g. "C:/folder/another folder"To load the data, please use:
In some cases, it is necessary to use individual dilution factors, Raman areas or pathlengths. This data is read using the base R function read.table. Please check that the column separator of your file is the same as in read.table (sep, which is defined as blank space here, hence sep = “ “). The same is true for the decimal separator of your numbers (dec, which is defined as dec = “,” in our case). Here, we import a table containing meta data provided with the package as an example. In the example only dilution data is provided via this table.
metatable <- system.file("extdata/metatable_dreem.csv",package = "staRdom") # path to example data, can be replaced by a path to your own data
meta <- read.table(metatable, header = TRUE, sep = ",", dec = ".", row.names = 1) # load dataIf you have not created a table containing meta data, you can use
eem_metatamplate to create a new one. It can be written to
a file using write.csv. Here is an example:
Check data
The eem_checkdata function prints out sample names and
folders, where possible problems are detected. Additionally a named list
with these sample names can be saved (variable problem in
the example code below).
The data can be checked for possible incorrect entries (in brackets names of the according list elements):
NAs (‘Not Available’ / missing values) in data (
NAs_in_EEMs)wavelength range mismatches (in-between EEMs:
EEMs_more_data_than_smallest, absorbance spectrum smaller than EEM spectrum:EEM_absorbance_wavelength_range_mismatch). Concerning wavelength spectra, only the range is important since values in-between are interpolated automatically for absorbance data and can be interpolated manually for different EEM samples using the functioneem_extend2largestwithinterpolation = TRUE.missing data (EEM but no absorbance:
EEMs_missing_absorbance, absorbance but no EEM:Absorbance_missing_EEMs, EEM but no metadata:EEMs_missing_metadata,metadata but no EEM:Metadata_missing_EEMs)inconsistencies (duplicates, invalid)in samples names between EEM, absorbance and metadata (e.g. samples missing in one of the three sets), (
Duplicate_EEM_names,Duplicate_absorbance_names,invalid_EEM_names,invalid_absorbance_names,Duplicates_metatable_names)not applied correction methods (
missing_data_correction).
Possible_problem_found is a logic variable in the list,
stating whether a possible problem was found or not.
In case of problems, you need to reorganise your data manually and
revise the steps mentioned above. The eem_checkdata
function can be run any time during the process to see if any changes in
the dataset caused inconsistencies. No correction of these problems is
done automatically!
## NAs were found in the following samples (ratio):
## d423sf (0), d457sf (0), d492sf (0), d667sf (0), dblank_di25se06 (0), d433sf (0), d437sf (0), d441sf (0), dblank_mq11my (0.02),
## Please consider interpolating the data. It is highly recommended, due to more stable and meaningful PARAFAC models!
## EEM samples missing absorbance data:
## dblank_di25se06 in
## /tmp/Rtmpbt18qR/Rinst18ba25f310a0/staRdom/extdata/EEMs//di25se06
## dblank_mq11my in
## /tmp/Rtmpbt18qR/Rinst18ba25f310a0/staRdom/extdata/EEMs//mq11myEEM data can contain NAs to perform a PARAFAC analysis as long as there is a certain amount of numeric values present. Depending on the data set, more than 15 to 20 % might cause non-converging models or models converging in a lokal minimum. We always suggest an interpolation of the data to get good results and a stable PARAFAC modelling process (Elcoroaristizabal et al. 2015).
Different EEM sizes are not a problem, because there is a way to address this as shown below. For a blank subtraction or a PARAFAC analysis, the available data for each sample must be similar.
The above mentioned absence of absorbance data for the blank samples can be justified, as absorbance of ultrapure water is theoretically 0 over the complete spectrum. In the further analysis, this is no problem.
Data preparation and correction
If you have used the template for the peak picking (vignette for basic
analysis), the correction is already done and you can start a
PARAFAC analysis with the eem_list resulting from this
template.
If either of the correction steps was already done (e.g. by the instrument), the specific correction step can just be skipped. In this case R might still tell you about missing correction steps and warnings might appear, but these can be ignored as long as the whole correction was done as desired.
Sample names
If you want to change your sample names, you can use
eem_name_replace. In the example, “(FD3)” is removed as it
is not part of the samples names but originates from the conversion of
Hitachi FD3 files to txt files. You can use this function for any
replacement in file names. Regular expressions (please see the help
on regular expressions) can be used in search and replace patterns
provided.
Absorbance baseline correction
The instrumental baseline drift in absorbance data can be corrected by subtracting the mean of the absorbance at high wavelengths (Li and Hur 2017). The default is to use the spectrum between 680 and 700 nm but any other range can be set manually.
Spectral correction
Spectral correction is done to remove instrument-specific influences
on the EEMs (DeRose and Resch-Genger
2010). Some instruments can do this automatically. The example
EEMs are corrected using eem_spectral_cor. Correction
vectors have to be provided in the same range as the EEM measurements.
If this is not the case, the EEMs can be cut to this range using
eem_range.
excorfile <- system.file("extdata/CorrectionFiles/xc06se06n.csv",package="staRdom")
Excor <- data.table::fread(excorfile)
emcorfile <- system.file("extdata/CorrectionFiles/mcorrs_4nm.csv",package="staRdom")
Emcor <- data.table::fread(emcorfile)
# adjust range of EEMs to cover correction vectors
eem_list <- eem_range(eem_list,ex = range(Excor[,1]), em = range(Emcor[,1]))
eem_list <- eem_spectral_cor(eem_list,Excor,Emcor)Blank subtraction
Blanks are samples of ultrapure water that must contain either “nano”, “miliq”, “milliq”, “mq” or “blank” in their file names. They can be used to apply blank subtractionand Raman normalisation (see below) and are used for samples in the same (sub)folders. If multiple blanks were measured, they are averaged. The example data consist of only two folders with one blank each. Blanks are subtracted from each sample to reduce the effects of scatter bands and systematic errors (Murphy et al. 2013).
The blanks must be the same size as the samples they will be subtracted from. As different sample sizes were reported above, all samples will be brought to the same data range before. You can find a description on data and wavelength ranges below.
# extending and interpolation data
eem_list <- eem_extend2largest(eem_list, interpolation = 1, extend = FALSE, cores = cores)
# blank subtraction
eem_list <- eem_remove_blank(eem_list)## A total of 1 blank EEMs will be averaged.
## A total of 1 blank EEMs will be averaged.## [[1]]
Inner-filter effect correction
Inner-filter effects (IFE) occur when excitation light is absorbed by chromophores. A simple method to correct the IFE is to use the sample’s absorbance. The EEM is multiplied by a correction matrix corresponding to each wavelength pair (Kothawala et al. 2013). In case of a maximum absorbance larger than 1.5 cm⁻¹, the sample needs to be diluted, because the absorbance is to high to be corrected by the applied IFE function (or mathematical IFE correction in general). The example uses a path length of 5 cm (5 cm long cuvettes) for absorption measurements.
In the example below, there is a warning about no absorbance data for the blank samples. This warning is not a problem because in ultrapure water samples there is practically no IFE and the sample is removed in the further analysis.
## d423sf
## Range of IFE correction factors: 1.0004 1.0288
## Range of total absorbance (Atotal) : 1e-04 0.0049
##
## d457sf
## Range of IFE correction factors: 1.0003 1.0208
## Range of total absorbance (Atotal) : 1e-04 0.0036
##
## d492sf
## Range of IFE correction factors: 1.0004 1.0241
## Range of total absorbance (Atotal) : 1e-04 0.0041
##
## d667sf
## Range of IFE correction factors: 1.0004 1.0249
## Range of total absorbance (Atotal) : 1e-04 0.0043## Warning in FUN(X[[i]], ...): No absorbance data was found for sample
## dblank_di25se06!No absorption data was found for sample dblank_di25se06!## d433sf
## Range of IFE correction factors: 1.0003 1.0241
## Range of total absorbance (Atotal) : 1e-04 0.0041
##
## d437sf
## Range of IFE correction factors: 1.0002 1.0131
## Range of total absorbance (Atotal) : 0 0.0023
##
## d441sf
## Range of IFE correction factors: 1.0002 1.016
## Range of total absorbance (Atotal) : 0 0.0028## Warning in FUN(X[[i]], ...): No absorbance data was found for sample
## dblank_mq11my!No absorption data was found for sample dblank_mq11my!## [[1]]
Raman normalisation
Fluorescence intensities can differ between analyses on different fluorometers, different settings or different days on the same fluorometer. Therefore it can be normalised to a standard scale of Raman Units by dividing all intensities by the area of the Raman peak of a ultrapure water sample. All fluorescence intensities are divided by the area (integral) of the Raman peak (excitation of 350 nm between an emission of 371 nm and 428 nm) (Lawaetz and Stedmon 2009). Values are interpolated if the wavelengths are missing.
You can use blanks, numeric values or data frames as source for the values. In case you use blank samples, again the blanks in the same sub-folder as the sample are used. Blanks are recognised by having “blank”, “miliq”, “milliq”, “nano” or “mq” in the file name. This means regular samples must not have it.
## A total of 1 blank EEMs will be averaged.## Raman area: 5687348
## Raman area: 5687348
## Raman area: 5687348
## Raman area: 5687348## A total of 1 blank EEMs will be averaged.## Raman area: 5688862
## Raman area: 5688862
## Raman area: 5688862## [[1]]
Raman areas can be calculated separately with the function
eem_raman_area.
Remove blanks from sample set
From this step onwards, blanks are not needed anymore. You can remove
them from your sample set. eem_extract removes all samples
including “nano”, “miliq”, “milliq”, “mq” or “blank” in their sample
names. select of the package dplyr can do the same for the
absorbance data.
## Removed sample(s): dblank_di25se06 dblank_mq11myRemove and interpolate scattering
The function removes scattering from the samples.
remove_scatter is a logical vector where values are ordered
by the meaning of “raman1”, “raman2”, “rayleigh1” and “rayleigh2”.
remove_scatter_width is either a number or a vector
containing 4 different wavelength width in nm, one for each scatter type
(Murphy et al. 2013; Lakowicz 2006).
remove_scatter <- c(TRUE, TRUE, TRUE, TRUE)
remove_scatter_width <- c(15,15,15,15)
eem_list <- eem_rem_scat(eem_list, remove_scatter = remove_scatter, remove_scatter_width = remove_scatter_width)## [[1]]
Although it is not always necessary, removed scatter areas should be
interpolated for reasonable results and faster calculation in the
PARAFAC analysis (Elcoroaristizabal et al.
2015). eem_interp offers different methods of
interpolation. The types of interpolation are (0) setting all NAs to 0,
(1) spline interpolation with mba.points (Lee, Wolberg, and Shin 1997), (2) excitation
and emission wavelength-wise interpolation with pchip (Moler 2004) and subsequent mean,
(3) excitation wavelength-wise interpolation with pchip and
(4) linear excitation and emission wavelength-wise interpolation with
na.approx and again subsequent mean
calculation. Calculating the mean is a way of ensuring NAs are also
interpolated where missing boundary values would make that impossible.
In case of interpolation type 1, extend = FALSE prevents
the function from extrapolating. We recommend to use type 1 as a start,
because its accuracy in interpolating surfaces. The smooth but still
complex surface is exactly what one would expect from a theoretical EEM.
In case of recognisable patterns in the residual plots close to the
scatter areas or many not converging initialisations of the PARAFAC
model, another interpolation method could improve the results.
## [[1]]
Correct for dilution
Data are corrected for dilution via eem_dilution. Each
EEM is multiplied with a dilution factor (e.g. 10 if 1 part sample was
diluted with 9 parts ultrapure water). Either a single numeric value for
all samples or a table with a specific value for each sample is
used.
This step can also be done manually after calculating peaks, indices and PARAFAC components. By that, a slightly different result has to be expected if EEMs are not normalised prior to creating a PARAFAC model. In other cases there is no difference whether EEMs or results are multiplied by the dilution factor.
Smooth data
Depending on your instrument, smoothing the data could be beneficial
for peak picking. For PARAFAC analysis smoothing is not advised. The
parameter n specifies the moving average window size in
nm.
Overview of samples
summary prints an overview of the samples containing
data ranges, applied correction methods and the manufacturer of the
instrument.
## sample ex_min ex_max em_min em_max is_blank_corrected is_scatter_corrected
## 1 d423sf 230 455 290 702 TRUE TRUE
## 2 d457sf 230 455 290 702 TRUE TRUE
## 3 d492sf 230 455 290 702 TRUE TRUE
## 4 d667sf 230 455 290 702 TRUE TRUE
## 5 d433sf 230 455 290 702 TRUE TRUE
## 6 d437sf 230 455 290 702 TRUE TRUE
## 7 d441sf 230 455 290 702 TRUE TRUE
## is_ife_corrected is_raman_normalized
## 1 TRUE TRUE
## 2 TRUE TRUE
## 3 TRUE TRUE
## 4 TRUE TRUE
## 5 TRUE TRUE
## 6 TRUE TRUE
## 7 TRUE TRUEPeak picking and indices
Peaks and indices known from the literature (Huguet et al. 2009; Zepp, Sheldon, and Moran 2004; McKnight et al. 2001; Ohno 2002) can be calculated.
If wavelength ranges needed for certain indices or peaks (e.g. the
humification index (HIX) uses an excitation wavelength of 254 nm, but
EEMs usually contain measurements at 250 and 255 nm) an interpolation is
done automatically between existing measurements (no extrapolation!).
This will be reported with warnings, however, these warnings can be
ignored. The smoothed EEMs eem4peaks are used for the
calculation. To extract individual peaks, the function
eem_peaks can be used.
bix <- eem_biological_index(eem4peaks)
coble_peaks <- eem_coble_peaks(eem4peaks)
fi <- eem_fluorescence_index(eem4peaks)
hix <- eem_humification_index(eem4peaks, scale = TRUE)
indices_peaks <- bix %>%
full_join(coble_peaks, by = "sample") %>%
full_join(fi, by = "sample") %>%
full_join(hix, by = "sample")
indices_peaks## sample bix b t a m c
## 1 d423sf 0.7238682 0.036238767 0.06222814 0.2799546 0.14974696 0.11645331
## 2 d457sf 0.6858719 0.023536584 0.04106616 0.2082118 0.11265412 0.08778000
## 3 d492sf 0.6869648 0.027140701 0.04730339 0.2413028 0.13198615 0.10493114
## 4 d667sf 0.6839838 0.031426888 0.05391093 0.2774084 0.14513535 0.13263827
## 5 d433sf 0.6941625 0.012110049 0.03792344 0.2147849 0.11547600 0.09000859
## 6 d437sf 0.6678838 0.006024978 0.02159146 0.1516322 0.07649198 0.06366574
## 7 d441sf 0.6670705 0.007355762 0.02692251 0.1882532 0.09387812 0.07938853
## fi hix
## 1 1.151716 0.8805637
## 2 1.143778 0.8923698
## 3 1.161794 0.8949828
## 4 1.139740 0.8965758
## 5 1.155606 0.9143584
## 6 1.116053 0.9420593
## 7 1.108152 0.9395073Absorbance indices
abs_parms can be used to calculate a254, a300, E2:E3,
E4:E6, S275-295, S350-400, S300-700, SR and the wavelength distribution
of absorption spectral slopes (Helms et al. 2008;
Twardowski et al. 2004; Massicotte 2016; Loiselle et al. 2009).
Li and Hur (2017) give a broad overview of
possible values and their applications used in recent literature.
Missing wavelengths, needed for certain indices or ratios are
interpolated automatically.
## sample a254 a300 E2_E3 E4_E6 S275_295 S350_400 S300_700
## 1 d423sf 13.869423 6.341582 7.275041 54.45985 0.01693705 0.01767518 0.01757271
## 2 d433sf 11.629678 5.354673 7.195549 67.97273 0.01685673 0.01775750 0.01764950
## 3 d437sf 6.323142 2.836798 7.235020 39.38501 0.01750176 0.01674770 0.01719949
## 4 d441sf 7.703282 3.396527 7.572209 39.06406 0.01776943 0.01723729 0.01747484
## 5 d457sf 10.051932 4.654212 7.091301 71.26347 0.01675176 0.01752695 0.01741157
## 6 d492sf 11.652366 5.424564 7.060283 73.15475 0.01665879 0.01754663 0.01743985
## 7 d667sf 12.048233 5.542739 7.063998 35.38728 0.01648855 0.01797665 0.01702009
## SR
## 1 0.9582393
## 2 0.9492738
## 3 1.0450242
## 4 1.0308717
## 5 0.9557717
## 6 0.9494014
## 7 0.9172203Creating a PARAFAC model
Finding an appropriate PARAFAC model is an iterative process. For comparing different methods, we used the same dataset and analysis procedure as in the drEEM tutorial which is a supplement to Murphy et al. (2013).
Loading data
Load drEEM example dataset
For this tutorial the drEEM example data is used. The complete and corrected data is downloaded from https://gitlab.com/dreem/drEEM and converted into an eemlist in R. The example PARAFAC models are calculated based on this complete sample set. You can also adapt that code to import any Matlab EEM data to staRdom.
dreem_raw <- tempfile()
download.file("https://gitlab.com/dreem/drEEM/-/raw/master/tutorials_demos/datasets/PortSurveyData_corrected.mat?inline=false",dreem_raw)
dreem_data <- dreem_raw %>%
R.matlab::readMat()
unlink(dreem_raw)
eem_list <- lapply(dreem_data$filelist.eem, function(file){
#file <- dreem_data$filelist.eem[1]
n <- which(dreem_data$filelist.eem == file)
file <- file %>%
gsub("^\\s+|\\s+$", "", .) %>% # trim white spaces in filenames
sub(pattern = "(.*)\\..*$", replacement = "\\1", .) # remove file extension from sample name
eem <- list(file = paste0("drEEM/dataset/",file),sample = file,x = dreem_data$XcRU[n,,] %>% as.matrix(),ex = dreem_data$Ex %>% as.vector(), em = dreem_data$Em.in %>% as.vector(), location = "drEEM/dataset/")
class(eem) <- "eem"
attr(eem, "is_blank_corrected") <- TRUE
attr(eem, "is_scatter_corrected") <- FALSE
attr(eem, "is_ife_corrected") <- TRUE
attr(eem, "is_raman_normalized") <- TRUE
attr(eem, "manufacturer") <- "unknown"
eem
}) %>%
`class<-`("eemlist")
# add sample name suffix, R has sometimes troubles, when sample names start with a number.
eem_names(eem_list) <- paste0("d",eem_names(eem_list))In the drEEM tutorial, all samples containing “bl” or “0A” are removed from the set.
ol <- function(x){x==("bl") | x == "0A"}
extract <- dreem_data$sites %>% unlist() %>% ol() %>% which()
eem_list <- eem_list %>% eem_extract(extract)Scattering has still to be removed and is done as described above.
eem_list <- eem_rem_scat(eem_list, remove_scatter = c(TRUE, TRUE, TRUE, TRUE), remove_scatter_width = c(15,15,18,19), interpolation = FALSE, cores = cores)If you have worked with the basic analysis template,
you can use the resulting data right away. In the case you did the
corrections with different sample sets separately and want to combine
them, you can use eem_import_dir to combine EEM samples
from several RData or RDa files. Put all files in one folder and run the
following:
Due to package size issues, no example data is included for this function.
We recommend using eem_checkdata again before continuing
the further analysis!
Sample set wavelength ranges
For a PARAFAC analysis, all samples of the set need to be similar in terms of provided wavelength pairs. In case you have deviating samples there are ways to solve this:
eem_extend2largestadds NAs if values present in another sample are missing (e.g. different wavelength slits or spectra ranges were used). These values can be interpolated.eem_red2smallestremoves wavelengths, that are missing in at least one sample form the whole set.
Find and remove noise in EEM data
An important way of finding noise in EEM data is viewing the samples.
You can use the function eem_overview_plot to view all your
samples in a convenient way. With the following functions, data can be
removed or set to NA (NAs are theoretically no problem for the PARAFAC
algorithm, but the calculation process and the results are often more
convient without) in different ways, or be interpolated, depending on
what you would like to do:
eem_extractremoves whole samples either by name or by number.eem_rangeremoves data outside the given wavelength ranges in all samples.eem_excluderemoves data from the sample set, provided by a list.eem_rem_scatandeem_remove_scatteringare used to set data in Raman and Rayleigh scattering of 1st and 2nd order to NA. While the later on removes one scattering at a time, the first one wraps it up to remove several scatterings in one step.eem_setNAreplaces data by NA in rectangular shape and in specific samples.eem_matmultmultiplies each EEM matrix by a certain matrix. This matrix can be used to set parts of the data to 0 or NA (e.g. the area where emission wavelength is shorter than excitation wavelength).eem_interpis used to interpolate data previously set to NA.
Sample “d667sf” will be used to show this process graphically. To extract the sample the regular expression “^d667sf$” is used. ^ stands for the beginning of the string and $ for the end and ensure an exact match. If you do not use these characters, all samples containing the string in their name are extracted.
This is where we start from:
The noisy range below 250 nm excitation and above 580 nm emission can be removed from the samples with the following command. As mentioned above, this was already removed in the example data.
Visually found irregularities in patterns are manually replaced by NA
and interpolated. From the sample “d667sf” a band covering the
excitation wavelengths from 245 to 350 is removed and a rectangle
covering emission wavelengths 560 to 576 and excitation wavelengths 280
to 295 is removed in all samples. For demonstration reasons, the
interpolation is done in an extra step but can also be included in the
removing function right away (interpolate = TRUE).
eem_list <- eem_list %>%
eem_setNA(sample = 176, ex = 345:350, interpolate = FALSE) %>%
eem_setNA(em = 560:576, ex = 280:295, interpolate = FALSE)Here, we show the changes, made to sample d667sf by the demonstrated
steps above (including the removing of the scatter):
Explore dataset
It is crucial to find an appropriate number of components in the analysis. If the number of components is too large, it may be the case that one component was split into two; if it is too low, relevant components may get lost (Murphy et al. 2013). To help you find the appropriate number, a series of PARAFAC models can be calculated and compared. In this example 5 models with 3 to 7 components are calculated.
The alternating-least-squares algorithm used to calculate the PARAFAC
model optimises the components in order to minimise the residual error.
The goal is to find a global minimum of the residual function. Depending
on the random start values (random initialisation), different local
minima can be found. To get the global minimum, a defined number
nstart of initialisations is used for separate model
calculations. The model with the smallest error is then used for further
analyses, assuming it is a global minimum. 25 might by a good start for
nstart although for a profound analysis higher values
(e.g. 50) are suggested.
Some of these random initialisations might not converge. If there are
still enough converging models, the result is reliable and there is no
problem. eem_parafac returns a warning in case of less than
50 % converging models. Furthermore, it is possible to calculate a
specific number of converging models by setting the argument
strictly converging = TRUE. When using this, due to the
iterative restarting of not converging models, this takes more time and
using more starts from the beginning is a faster way to get a reasonable
number of converging models.
You can speed up the calculations by using multiple
cores. Beware, that calculating a PARAFAC model can take
some time!
Higher maxit (maximum number of iteration steps in
PARAFAC) and lower ctol (tolerance to return result of
PARAFAC, should not be larger than 10⁻⁶) increase the accuracy of the
model but take more computation time. For a final model, we suggest to
use a tolerance of 10⁻⁸ to 10⁻¹⁰.
In this first model creation step, the constraints are tested. While
pf1 is calculated without any constraints,
pf1n uses the assumption that modes are non-negative only.
This is a very common assumption, because fluorescence cannot be
negative. Common constraints are none (“uncons”), non-negative
(“nonneg”) and unimodal, non-negative (“uninon”). Besides these, other
possible constraints can be seen using the command
CMLS::const().
PARAFAC modes can be rescaled so that their maximum is 1 and effects
are more visible in the plots. The rescaling is corrected in the A mode
(sample mode). In case of uneven peak heights,
eempf_rescaleBC can help to improve the visibility of your
graphs. The parameter newscale specifies the root
mean-squared error of each column in matrices B and C. This is
compensated in the A mode (sample mode). Alternatively
newscale can be set "Fmax"; each peak has a
height of 1 then.
The PARAFAC models created below can be loaded from the staRdom package’s example data instead of calculating it:
nstart <- 25 # number of similar models from which best is chosen
maxit = 5000 # maximum number of iterations in PARAFAC analysis
ctol <- 10^-6 # tolerance in PARAFAC analysis
# calculating PARAFAC models, one for each number of components
pf1 <- eem_parafac(eem_list, comps = seq(dim_min,dim_max), normalise = FALSE, const = c("uncons", "uncons", "uncons"), maxit = maxit, nstart = nstart, ctol = ctol, cores = cores)
# same model but using non-negative constraints
pf1n <- eem_parafac(eem_list, comps = seq(dim_min,dim_max), normalise = FALSE, const = c("nonneg", "nonneg", "nonneg"), maxit = maxit, nstart = nstart, ctol = ctol, cores = cores)
# rescale B and C modes to a maximum fluorescence of 1 for each component
pf1 <- lapply(pf1, eempf_rescaleBC, newscale = "Fmax")
pf1n <- lapply(pf1n, eempf_rescaleBC, newscale = "Fmax")Use eempf_compare to plot the created models’
components. You can see the models fits and components (rows) for models
with different numbers of components (columns) in 2 different views. The
single plots can be created using eempf_fits and
eempf_plot_comps.
# This plot is not shown, because the components violate the assumptions for fluorescence peaks (negative fluorescence). Please try, if you are interested.
eempf_compare(pf1, contour = TRUE)
## [[1]]
##
## [[2]]
##
## [[3]]
Check the correlation between different components
The PARAFAC algorithm assumes no correlation between the components.
If samples are in a wide range of DOC concentrations, a correlation of
the components is likely. To avoid that, the samples can be normalised.
The model with 6 components (4th model in the list, therefore
[[4]]) is used for now.
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## Comp.1 1.0000000 0.9914361 0.8362761 0.7299886 0.9290694 0.9892667
## Comp.2 0.9914361 1.0000000 0.7848764 0.6543362 0.9489413 0.9878114
## Comp.3 0.8362761 0.7848764 1.0000000 0.8506471 0.8085888 0.8152542
## Comp.4 0.7299886 0.6543362 0.8506471 1.0000000 0.5488814 0.7064891
## Comp.5 0.9290694 0.9489413 0.8085888 0.5488814 1.0000000 0.9210369
## Comp.6 0.9892667 0.9878114 0.8152542 0.7064891 0.9210369 1.0000000
As some of the components are highly correlated, the model is
calculated again with normalised sample data. Later normalisation is
reversed automatically by multiplying the A modes (samples loadings)
with the normalisation factors for exports and plots. Reversing
normalisation can be done manually applying norm2A. The
parameter normalisation in eempf_cortable and
eempf_corplot is set FALSE (default) if the
model quality is to be assessed. For interpretations and patterns in the
actual fluorescence in your samples normalisation has to be
set TRUE to see the actual values.
pf2 <- eem_parafac(eem_list, comps = seq(dim_min,dim_max), normalise = TRUE, const = c("nonneg", "nonneg", "nonneg"), maxit = maxit, nstart = nstart, ctol = ctol, cores = cores)
# rescale B and C modes
pf2 <- lapply(pf2, eempf_rescaleBC, newscale = "Fmax")# eempf_compare(pf2, contour = TRUE) # use this to show the same plot as above
# for now, we are happy with just the components
eempf_plot_comps(pf2, contour = TRUE, type = 1)
Find and exclude outliers leverage
The leverage is calculated by eempf_leverage and can be
plotted with eempf_leverage_plot. Using
eempf_leverage_ident to plot the leverage shows an
interactive plot where you can click on certain values to save them in a
variable. Three plots (samples, excitation, emission) show up one after
the other. You can select wavelengths or samples by clicking on the
certain point in the plot and click ‘Finish’ when you are done. The
variable exclude in the example contains all selected
values. The returned list can directly be used to exclude the outliers
using eem_exclude (see above). qlabel defines
the size of the upper quantile that is labelled in the plots.
eempf_mleverage can be used to compare the leverages of
samples in different models.
# calculate leverage
cpl <- eempf_leverage(pf2[[4]])
# plot leverage (nice plot)
eempf_leverage_plot(cpl,qlabel=0.1)
# plot leverage, not so nice plot but interactive to select what to exclude
# saved in exclude, can be used to start over again with eem_list_ex <- eem_list %>% eem_exclude(exclude) above
exclude <- eempf_leverage_ident(cpl,qlabel=0.1)In order to save the decisions of the graphical outlier determination not only as a variable but also in a script, we advise to generate the exclude list manually. This can help you following your way later. See example below.
# samples, excitation and emission wavelengths to exclude, makes sense after calculation of leverage
exclude <- list("ex" = c(),
"em" = c(),
"sample" = c("dsfb676psp","dsgb447wt")
)
# exclude outliers if neccessary. if so, restart analysis
eem_list_ex <- eem_exclude(eem_list, exclude)A new PARAFAC model is then generated without outliers:
pf3 <- eem_parafac(eem_list_ex, comps = seq(dim_min,dim_max), normalise = TRUE, maxit = maxit, nstart = nstart, ctol = ctol, cores = cores)
pf3 <- lapply(pf3, eempf_rescaleBC, newscale = "Fmax")
Examine residuals
The outliers determined above are included to show the difference in residuals. Analysing these residuals can show deficits in model creation, problems with sample handling and lab equipment or it can already be helpful in answering scientific questions.
eempf_residuals_plot(pf3[[4]], eem_list, residuals_only = TRUE, select = c("d0680sfK", "d1266sf", "d1268sfK", "d1543sfK", "dsfb676psp", "dsgb447wt"), spp = 6, cores = cores, contour = TRUE)## Removed sample(s): d1549sfK d1550sfK d1557sfK d1559sfK d1565sfK d1567sfK d1568sfK d492sf d661sf d667sf dSFB445pwd1tRecalculating the model with increased accuracy
Due to long calculation times with higher accuracy in the model
calculation, the tolerance is only increased in the last step. Just the
model with 6 components is recalculated. We use
strictly_converging = TRUE here to derive a meaningful
number of truly converging models. If you set this argument to
FALSE, please check the ratio of converging models to be
sure, the best is chosen from a reasonably high number.
ctol <- 10^-8 # decrease tolerance in PARAFAC analysis
nstart = 20 # number of random starts
maxit = 10000 # increase number of maximum interations
pf4 <- eem_parafac(eem_list_ex, comps = 6, normalise = TRUE, const = c("nonneg", "nonneg", "nonneg"), maxit = maxit, nstart = nstart, ctol = ctol, output = "all", cores = cores, strictly_converging = TRUE)
pf4 <- lapply(pf4, eempf_rescaleBC, newscale = "Fmax")Check the convergence behaviour of the created models:
## Calculated models: 20
## Converging models: 20
## Not converging Models, iteration limit reached: 0
## Not converging models, other reasons: 0
## Best SSE: 378.6088
## Summary of SSEs of converging models:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 378.6 379.1 379.4 10664.2 380.8 205317.8eempf_leverage_plot(eempf_leverage(pf4[[1]])) # [[1]] means the 4th model in the list, 6 component model in that case
It is possible to use the results from a previous model as starting
conditions (Astart, Bstart and
Cstart). Supplying start matrices is only possible if a
model with the same number of components, excitation and emission
wavelengths is calculated. If samples differ (e.g. outlier removal or
inclusion) simply remove the Astart. In the example, we set
up a very rough model using a reduced tolerance but a lot of random
starts. In case of doubts, do not use start matrices!
# calculating a rough model, nstart is high (100) but ctol is 2 magnitudes larger or at least 0.01
pf5 <- eem_parafac(eem_list, comps = 6, normalise = TRUE, const = c("nonneg", "nonneg", "nonneg"), maxit = maxit, nstart = 100, ctol = min(ctol*100,0.01), cores = cores)
# plot is not shown
ggeem(pf5[[1]], contour = TRUE)
nstart <- 5
pf4 <- eem_parafac(eem_list_ex, comps = 6, normalise = TRUE, const = c("nonneg", "nonneg", "nonneg"), maxit = maxit, nstart = nstart, ctol = ctol, cores = cores, Bstart = pf5[[1]]$B, Cstart = pf5[[1]]$C)
pf4 <- lapply(pf4, eempf_rescaleBC, newscale = "Fmax")
# plot is not shown
ggeem(pf4[[1]], contour = TRUE)Please redo the steps dscribed in the section “Creating a PARAFAC model” until you are satisfied with the results.
Plot the resulting components and loadings
The following plot shows the shape of the determined components and the loadings in the different samples. The components’ shapes are important for an interpretation from a chemical point of view. The loadings show the fluorescence differences of different components in different samples.
## [[1]]
##
## [[2]]
Separate plots can be generated by using ggeem for
components and eempf_load_plot for the loadings.
It is possible to view the components in 3D using
eempf_comps3D.
Plotting samples and residuals
The plots show samples in columns and the rows show the components (6 in that case), the residuals and the whole sample.
# plot components in each sample, residual and whole sample
eempf_residuals_plot(pf4[[1]], eem_list, select = eem_names(eem_list)[10:14], cores = cores, contour = TRUE)## [[1]]
Split-half analysis
The split-half analysis is intended to show the stability of your model. The data is recombined in 6 different ways and results from each sub-sample should be similar (Murphy et al. 2013).
#calculate split_half analysis
sh <- splithalf(eem_list_ex, 6, normalise = TRUE, rand = FALSE, cores = cores, nstart = nstart, strictly_converging = TRUE, maxit = maxit, ctol = ctol)Split-half analysis takes some time, so the results are included in the package.
Plot the results from the split-half analysis. Your model is stable, if the graphs of all components look similar.
# you can also use the already known plots from eempf_compare
# sh %>% unlist(recursive = FALSE) %>% eempf_compare()If some splits look similar (or see below, have a Tucker’s congruency
coefficient close to 1) and others do not, this is a strong hint that
the particular splits or the values for maxit and
nstart might be responsible for unstable conditions.
Problems can be caused by splitting the data according to natural
differences (e.g. sampling date A and sampling date B) which will then
lead to different PARAFAC models. Changing these manually (using the
parameter splits = ...) or randomly
(rand = TRUE, used in the example below) can help in that
case.
sh_r <- splithalf(eem_list_ex, 6, normalise = TRUE, rand = TRUE, cores = cores, nstart = nstart, maxit = maxit, ctol = ctol)Tucker’s Congruency Coefficients is a value for the similarity of the
splits (and different loadings in general) and
splithalf_tcc returns a table showing the values. 1 would
be perfect similarity.
## component comb tcc_em tcc_ex
## 1 Comp.1 ABvsCD 0.9999445 0.9945580
## 2 Comp.1 ACvsBD 0.9999615 0.9981481
## 3 Comp.1 ADvsBC 0.9999894 0.9926984
## 4 Comp.2 ABvsCD 0.9912625 0.9999952
## 5 Comp.2 ACvsBD 0.9966507 0.9999967
## 6 Comp.2 ADvsBC 0.9933854 0.9999739
## 7 Comp.3 ABvsCD 0.9988279 0.9765243
## 8 Comp.3 ACvsBD 0.9979108 0.9909373
## 9 Comp.3 ADvsBC 0.9974072 0.9942648
## 10 Comp.4 ABvsCD 0.9999394 0.9974468
## 11 Comp.4 ACvsBD 0.9999632 0.9969085
## 12 Comp.4 ADvsBC 0.9999590 0.9988635
## 13 Comp.5 ABvsCD 0.9999554 0.9994255
## 14 Comp.5 ACvsBD 0.9999649 0.9998939
## 15 Comp.5 ADvsBC 0.9998862 0.9995941
## 16 Comp.6 ABvsCD 0.9998451 0.9951453
## 17 Comp.6 ACvsBD 0.9998471 0.9961400
## 18 Comp.6 ADvsBC 0.9997503 0.9956836The function eempf_ssc can be used to compare models,
not only from a split-half analysis. It returns the shift- and
shape-sensitive congruence (SSC, Wünsch et al.
2019). Alternatively, the TCC can be calculated using the
attribute tcc = TRUE. TCCs and SSCs can be combined over
excitation and emission spectra using m = TRUE to calculate
the modified TCC (Parr et al. 2014) or
modified SSC respectively.
Loadings of outliers
A modes (loadings) of previously excluded outliers can be calculated
using A_missing. This should be used carefully, but enables
you to get loadings, that can be further investigated. Please supply an
eemlist containing all samples you are interested in. B- and C-modes of
the original model are kept and A-modes are calculated.
## Warning in A_missing(eem_list, pfmodel = pf4[[1]], cores = cores): The provided samples contain the following wavelengths that
## are not present in the PARAFAC model: Emission ; Excitation . These wavelengths were automatically removed.Further model validation
Core consistency
As a way of model validation, the core consistency can be calculated. Please see Murphy et al. (2013) for the limited usability of core consistency for model validation from natural EEMs.
EEMqual
EEMqual is a quality parameter integrating the model fit, the core consistency and the split-half analysis according to Bro and Vidal (2011). Due to the fact that the core consistency is included, the limitations are similar (see above).
Importance of components
Currently, there is not one particular way to determine the
importance of each component in a model. Still, answering this question
is interesting from an ecological point of view. Here, we propose one
way, that is commonly used in different modelling processes. You can
calculate the component importance using eempf_varimp.
Starting from the model you created, each component is removed at a time
and a new model is created using the exact previous components. The
difference between the original R-squared and the one from the new model
with one component reduced.
Formatting a model
Naming models and components
Models and components can be named. These names can be important for you to organise your models and interpretations of the components. They are also shown in the plots. Here are some examples:
## NULL# set new model names, number of models must be equal to number of names
names(pf3) <- c("3 components", "4 components xy","5 components no outliers","6 components","7 components")
names(pf3)## [1] "3 components" "4 components xy"
## [3] "5 components no outliers" "6 components"
## [5] "7 components"## [[1]]
## [1] "Comp.1" "Comp.2" "Comp.3" "Comp.4" "Comp.5" "Comp.6"# set new model names, number of models must be equal to number of names
eempf_comp_names(pf4) <- c("A4","B4","C4","D4","E4","F4")
# in case of more than one model(e.g. pf3):
eempf_comp_names(pf3) <- list(c("A1","B1","C1"), # names for 1st model
c("humic","T2","whatever","peak"),
c("rose","peter","frank","dwight","susan"),
c("A4","B4","C4","D4","E4","F4"),
c("A5","B5","C5","D5","E5","F5","G5") # names for 5th model
)
pf4[[1]] %>%
ggeem(contour = TRUE)
Sorting components
Components within a PARAFAC model can be reordered using
eempf_reorder.
Model export and interpretation
Comparing your data using openfluor.org
You can use eempf_openfluor to export a file that can be
uploaded to openfluor.org (Murphy et al.
2014). Please check the file header manually after export as some
values are not set automatically. Openfluor offers ways to compare your
components with those found in other publications. This is a very
important step in interpreting the results and coming to ecological
sound conclusions. Models can be directly uploaded to openfluor.org.
Please see the help of eempf_openfluor for details.
Comparing data using SSC
(Wünsch et al. 2019) showed, that the
TCC is sometimes not sensitive enough to separate different components.
Therefore, they developed the shift- and shape sensitive congruence
coefficient (SSC). It can be calculated using the function
eempf_ssc.
Creating a report on your analysis
The report created by eempf_report contains important
settings and results of your analysis and is exported as an html file.
You can specify the information you want to include.
Exporting the model
Using eempf_export you can export your model matrices to
a csv file.
eem_metatemplate is intended as a list of samples and a
template for a table containing metadata. Writing this table to a file
eases the step of gathering needed values for all samples.
Combine results and handle dilution issues
eem_dilcorr creates a table containing information on
how to handle diluted samples. Absorbance spectra need to be replaced by
undiluted measurements preferably or multiplied by the dilution factor.
Names of EEM samples can be adjusted to be similar to their undiluted
absorbance sample. You can choose for each sample how you want to
proceed on the command line. The table contains information about these
two steps.
eem_absdil takes information from the table generated by
eem_dilcorr and multiplies or deletes undiluted absorbance
sample data.
eem_eemdil takes information from the table generated by
eem_dilcorr and renames EEM samples to match undiluted
absorbance samples.
Experimental(!) functions
SSCs between initialisations
The shift- and shape sensitive congruence coefficient (SSC, Wünsch et al. 2019) (or TCC) between the
e.g. 3 to 6 best initialisations of the model could be an indicator to
evaluate the stability of the model creation process. If one of the
components is much different from the others, the best model is a lucky
guess. Models with several initialisations giving very similar results
are more trustworthy. You might overthink the modelling parameters and
the preprocessing. To do this test, you need to keep all created models
by adding the argument output = "all" to the
eem_parafac function.
pf4 <- eem_parafac(eem_list_ex, comps = 6, normalise = TRUE, const = c("nonneg", "nonneg", "nonneg"), maxit = maxit, nstart = nstart, ctol = ctol, output = "all", cores = cores)
ssccheck <- eempf_ssccheck(pf4[[1]]$models, best = 3, cores = cores) # best 3 models are shown
eempf_plot_ssccheck(ssccheck)Recombining components
Recombining the components of a PARAFAC model is generally not advised. It should be an opportunity for advanced users to work through their data, test hypothesis and find new approaches. The results from such a model have to be investigated in detail and differ significantly from models created in the traditional way. Please beware of using these functions!
Components can be extracted from models using
eempf_excomp. The extracted components can then be used to
create new models using A_missing and the
components argument.
References
- Introduction
- Example data coming with the package
- Import raw data
- Data preparation and correction
- Peak picking and indices
- Absorbance indices
- Creating a PARAFAC model
- Loading data
- Sample set wavelength ranges
- Find and remove noise in EEM data
- Explore dataset
- Check the correlation between different components
- Find and exclude outliers leverage
- Examine residuals
- Recalculating the model with increased accuracy
- Plot the resulting components and loadings
- Plotting samples and residuals
- Split-half analysis
- Loadings of outliers
- Further model validation
- Formatting a model
- Model export and interpretation
- Experimental(!) functions
- References