**2.2. Calibration**

### *2.2.1. Multiple Linear Regression (MLR)*

MLR is directed at modelling the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable X is associated with a value of the dependent variable Y, with explanatory or predictive purposes. A direct correlation between Y and X-matrix is performed.

In waste management MLR was applied by Chikae et al. [32] to predict the germination index which was adopted as a marker for compost maturity. Thirty-two parameters of 159 samples were measured. MLR was carried out to reduce this huge parameter set to some significant parameters. Lawrence and Boutwell [79] used MLR for predicting the stratigraphy of landfill sites using an electromagnetic method. Moreno-Santini et al. [80] applied MLR to determine arsenic and lead levels in the hair of residents in a municipality constructed on a former landfill.

Noori et al. [84] compared two different statistical methods (artificial neural networks and MLR based on a PCA) to predict the solid waste generation in Tehran. Cheng et al. [83] used MLR to predict the factors associated with medical waste generation at hospitals. Sun et al. [29] used MLR to predict mesophilic and thermopilic bacteria in food waste composts. Suehara and Yano [33] applied MLR to predict conventional compost parameters by NIR spectral data.

### *2.2.2. Partial Least Squares Regression (PLS-R)*

PLS1

22 Multivariate Analysis in Management, Engineering and the Sciences

Soft independent modelling of class analogy (SIMCA)

incinerator (MSWI) bottom ash before and after CO2 uptake. A DA on the CO2 ion current recorded during combustion was applied to illustrate the effect of CO2 treatment of MSWI bottom ash [66]. DA was also used to illustrate the spectral characteristics of leachate from

SIMCA is a special method of soft modelling recommended by Wold in the 1970s [88]. Objects can belong to one of the defined class, to both classes or to none. Whether SIMCA can be applied on the data set depends on the question to be answered. According to Brereton [88] it is often legitimate in chemistry that an object belongs to more than one class For example a compound may have an ester and an alkene group which are both reflected by an infrared spectrum. Thus they fit in both classes. In natural science it is allowed in most

Contrarily in other cases an object can belong only to one class and the application of SIMCA is inappropriate. Brereton [88] gives a good example where the concept of SIMCA is not applicable: A banknote is either forged or not. In many cases there is only one true

In compost science Malley et al. [8] and Smidt et al. [12] carried out a SIMCA. Malley et al. [8] classified different decomposition stages of manures by means of near infrared spectroscopy and SIMCA. Smidt et al. [12] carried out a SIMCA to classify different waste materials such as biowaste compost, mechanically-biologically pretreated waste and landfill materials based on their spectroscopic pattern. Smidt et al. [78] used the SIMCA model developed by Smidt et al. [12] to identify different landfill types such as reactor landfill and

MLR is directed at modelling the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable X is associated with a value of the dependent variable Y, with explanatory or predictive purposes. A direct correlation between Y and X-matrix is performed. In waste management MLR was applied by Chikae et al. [32] to predict the germination index which was adopted as a marker for compost maturity. Thirty-two parameters of 159 samples were measured. MLR was carried out to reduce this huge parameter set to some significant parameters. Lawrence and Boutwell [79] used MLR for predicting the stratigraphy of landfill sites using an electromagnetic method. Moreno-Santini et al. [80] applied MLR to determine arsenic and lead levels in the hair of residents in a municipality

Noori et al. [84] compared two different statistical methods (artificial neural networks and MLR based on a PCA) to predict the solid waste generation in Tehran. Cheng et al. [83] used

landfill simulation reactors under aerobic and anaerobic conditions [17].

cases for an object to be in line with more than one class simultaneously.

answer. For such problems SIMCA is not the adequate method.

industrial landfill samples.

*2.2.1. Multiple Linear Regression (MLR)* 

constructed on a former landfill.

**2.2. Calibration** 

PLS-R is used to find out the fundamental relations between two matrices. PLS-R is a bilinear modelling method. The main idea behind it is to calculate the principal components of the X and the Y matrix separately (external correlation) and to develop a regression model between the scores of the principal components (inner correlation). The concept of PLS-R is demonstrated in Fig. 3.

PLS1 is often used to predict time consuming or expensive parameters using an alternative analytical method. Modern analytical tools such as spectroscopic, chromatographic and thermo analytical methods generate data with inherent information on different parameters. With the development of an evaluated prediction model conventional analytical methods can be replaced by easier and/ or faster handling and robust methods.

**Figure 3.** Principles of PLS-R (according to Esbensen [85])

Many authors have developed such prediction models in compost science. Zvomuya et al. [44] predicted phosphorus availability in soils, amended with composted and noncomposted cattle manure by means of cumulative phosphorus analysis. Fujiwara and

Murakami [35] applied near infrared spectroscopy to estimate available nitrogen in poultry manure compost. Huang et al. [36] also used near infrared spectroscopy to estimate pH, electric conductivity, volatile solids, TOC, total N, the C:N ratio and the total phosphorus content. Furthermore they determined nutrient contents such as K, Ca, Mg, Fe and Zn of animal manure compost using near infrared spectroscopy and PLS1 [37]. Malley et al. [8] developed prediction models for total C, organic C, total N, C:N ratio, K, S and P by means of near infrared spectroscopy and PLS1. Morimoto et al. [43] carried out carbon quantification of green grass tissue using near infrared spectroscopy. Hansson et al. [6] predicted the concentration of propionate in an anaerobic process by near infrared spectra. Albrecht et al. [2] developed calibration models between spectral data and C, N, C:N ratio and composting time. Michel et al. [42] predicted chemical and biological properties of composts such as organic C (Corg), total N, C:N ratio, age, microbial biomass (Cmic), Cmic:Corg, basal respiration, enzymatic activity and plant suppression using near infrared spectroscopy. Ludwig et al. [39] also used near infrared spectroscopy to predict pH, electric conductivity, P, K, NO3 and NH4+ and phytotoxicity. Ko et al. [38] predicted heavy metal contents of Cr, As, Cd, Cu, Zn and Pb by means of near infrared spectroscopy and PLS1. They hypothesised that heavy metals are detectable by NIR when they are complexed with organic matter. Capriel et al. [34] found out that mid infrared spectroscopy is a rapid method to estimate the effect of nitrogen and relevant parameters such as total C, total N, the C:N ratio and the pH of biowaste compost. Meissl et al. [40] used PLS1 and the mid infrared region to predict humic acid contents in biowaste composts. Furthermore they determined humic acid contents by near infrared spectroscopy [41]. Sharma et al. [47] developed prediction models for conventional compost parameters, especially ammonia, pH, conductivity, dry matter, nitrogen and ash using NIR and Vis-NIR spectroscopy. Lillhonga et al. [23] used PLS-R for compost parameter prediction based on NIR spectra. They developed models for the parameters: time, pH, temperature, NH3/NH4+, energy (calorific value) and moisture content. Galvez-Sola et al. [45] used PLS1 to predict different compost quality parameters such as pH, electric conductivity, total organic matter, total organic carbon, total N, C/N ratio as well as nutrients contents (N, P, K) and potentially pollutant element concentrations (Fe, Cu, Mn and Zn) from near infrared spectra. Vergnoux et al. [21] applied a PLS1 to predict physico-chemical and biochemical parameters from NIR spectra. Physico-chemical parameters comprised age, organic carbon, organic nitrogen, C/N, total N, fulvic acids (FA), humic acids (HA) and HA/FA. The soluble fraction, lignin and biological maturity index were summarised as biochemical parameters. Mikhailov et al. [62] used PLS1 to predict maturity and stability based on conventionally measured data. Kylefors [61] developed prediction models for leachate concentrations of specific organic substances in leachate by means of conventional leachate analysis and PLS1. Biasioli et al. [19] used PLS1 to predict odour concentrations in composting plants by proton transfer reaction-mass spectrometry (PTR-MS). Mohajer et al. [46] used a PLS1 to generate a model to predict the microbial oxygen uptake in sludge based on different physical compost parameters.

Application of Multivariate Data Analyses in Waste Management 25

Böhm et al. [57] used PLS1 to predict the respiration activity (RA4) based on FT-IR spectra of mechanically-biologically pretreated (MBT) waste. The potential of thermal data of MBT waste was shown by Smidt et al. [53]. They applied PLS1 to predict the calorific value, total organic carbon (TOC) and respiration activity (RA4). Smidt et al. [17] also developed a prediction model for the calorific value based on spectral data. Biasioli et al. [58] used PLS1

Ecke et al. [71] performed detoxification of hexavalent chromium to less toxic trivalent chromium in industrial waste and applied a PLS model to identify the relevant factors. Smidt et al. [78] predicted the biological oxygen demand and the dissolved organic carbon (DOC) of old landfill materials from spectral data. They also used PLS-R to predict the total organic carbon and total nitrogen based on thermal data [78]. Furthermore PLS-R was used to predict respiration activity (RA4) from MS data of old landfill materials [66]. Smidt et al. [17] developed a prediction model for the DOC and the TOC from spectral data of landfill

PLS2 is a variant of the PLS-R method where several Y-variables are modelled simultaneously. An advantage of this method is to find possible correlations or co-linearity

Malley et al. [8] developed prediction models for pH, total N, nitrate and nitrite, total C, organic C, C:N ratio, P, available P, S, K and Na by means of near infrared spectroscopy and PLS2. Suehara et al. [48] used PLS2 for simultaneous measurement of carbon and nitrogen content of composts using near infrared spectroscopy. Vergnoux et al. [21] applied PLS2 to predict physico-chemical (moisture, temperature, pH, NH4-N) and biochemical parameters

This special regression method is described in Galvez-Sola et al. [49]. Galves Sola et al. [49]

**3. Selected examples from literature using multivariate data analysis in** 

In the following chapter four selected examples using multivariate data analysis in waste management are described in detail. To illustrate the application of principal component analysis (PCA) the study by Mikhailov et al. [62] is presented. He carried out multivariate data analysis for the ecological assessment of landfills. The second example illustrates the application of partial least squares regression (PLS-R). Michel et al. [42] applied PLS-R to predict conventional parameters by spectroscopic data. Ros et al. [27] applied a cluster analysis to data of polymerase chain reaction coupled with denaturing gradient gel electrophoresis (PCR-DGGE) to observe the long-term effects of compost amendment on soil microbial activity. A soft independent model of class analogy (SIMCA) was applied by Malley et al. [8]. They used SIMCA to classify different composts according to their spectroscopic characteristic.

to predict odour concentration from MSW composting plants based on PTR-MS.

materials. PLS2

between the Y-variables.

**waste management** 

(hemicellulose and cellulose) from NIR spectra.

used this method to predict the phosphorus content in composts.

Penalised signal regression (PSR)

Böhm et al. [57] used PLS1 to predict the respiration activity (RA4) based on FT-IR spectra of mechanically-biologically pretreated (MBT) waste. The potential of thermal data of MBT waste was shown by Smidt et al. [53]. They applied PLS1 to predict the calorific value, total organic carbon (TOC) and respiration activity (RA4). Smidt et al. [17] also developed a prediction model for the calorific value based on spectral data. Biasioli et al. [58] used PLS1 to predict odour concentration from MSW composting plants based on PTR-MS.

Ecke et al. [71] performed detoxification of hexavalent chromium to less toxic trivalent chromium in industrial waste and applied a PLS model to identify the relevant factors. Smidt et al. [78] predicted the biological oxygen demand and the dissolved organic carbon (DOC) of old landfill materials from spectral data. They also used PLS-R to predict the total organic carbon and total nitrogen based on thermal data [78]. Furthermore PLS-R was used to predict respiration activity (RA4) from MS data of old landfill materials [66]. Smidt et al. [17] developed a prediction model for the DOC and the TOC from spectral data of landfill materials.

PLS2

24 Multivariate Analysis in Management, Engineering and the Sciences

conductivity, P, K, NO3-

parameters.

Murakami [35] applied near infrared spectroscopy to estimate available nitrogen in poultry manure compost. Huang et al. [36] also used near infrared spectroscopy to estimate pH, electric conductivity, volatile solids, TOC, total N, the C:N ratio and the total phosphorus content. Furthermore they determined nutrient contents such as K, Ca, Mg, Fe and Zn of animal manure compost using near infrared spectroscopy and PLS1 [37]. Malley et al. [8] developed prediction models for total C, organic C, total N, C:N ratio, K, S and P by means of near infrared spectroscopy and PLS1. Morimoto et al. [43] carried out carbon quantification of green grass tissue using near infrared spectroscopy. Hansson et al. [6] predicted the concentration of propionate in an anaerobic process by near infrared spectra. Albrecht et al. [2] developed calibration models between spectral data and C, N, C:N ratio and composting time. Michel et al. [42] predicted chemical and biological properties of composts such as organic C (Corg), total N, C:N ratio, age, microbial biomass (Cmic), Cmic:Corg, basal respiration, enzymatic activity and plant suppression using near infrared spectroscopy. Ludwig et al. [39] also used near infrared spectroscopy to predict pH, electric

contents of Cr, As, Cd, Cu, Zn and Pb by means of near infrared spectroscopy and PLS1. They hypothesised that heavy metals are detectable by NIR when they are complexed with organic matter. Capriel et al. [34] found out that mid infrared spectroscopy is a rapid method to estimate the effect of nitrogen and relevant parameters such as total C, total N, the C:N ratio and the pH of biowaste compost. Meissl et al. [40] used PLS1 and the mid infrared region to predict humic acid contents in biowaste composts. Furthermore they determined humic acid contents by near infrared spectroscopy [41]. Sharma et al. [47] developed prediction models for conventional compost parameters, especially ammonia, pH, conductivity, dry matter, nitrogen and ash using NIR and Vis-NIR spectroscopy. Lillhonga et al. [23] used PLS-R for compost parameter prediction based on NIR spectra. They developed models for the parameters: time, pH, temperature, NH3/NH4+, energy (calorific value) and moisture content. Galvez-Sola et al. [45] used PLS1 to predict different compost quality parameters such as pH, electric conductivity, total organic matter, total organic carbon, total N, C/N ratio as well as nutrients contents (N, P, K) and potentially pollutant element concentrations (Fe, Cu, Mn and Zn) from near infrared spectra. Vergnoux et al. [21] applied a PLS1 to predict physico-chemical and biochemical parameters from NIR spectra. Physico-chemical parameters comprised age, organic carbon, organic nitrogen, C/N, total N, fulvic acids (FA), humic acids (HA) and HA/FA. The soluble fraction, lignin and biological maturity index were summarised as biochemical parameters. Mikhailov et al. [62] used PLS1 to predict maturity and stability based on conventionally measured data. Kylefors [61] developed prediction models for leachate concentrations of specific organic substances in leachate by means of conventional leachate analysis and PLS1. Biasioli et al. [19] used PLS1 to predict odour concentrations in composting plants by proton transfer reaction-mass spectrometry (PTR-MS). Mohajer et al. [46] used a PLS1 to generate a model to predict the microbial oxygen uptake in sludge based on different physical compost

and NH4+ and phytotoxicity. Ko et al. [38] predicted heavy metal

PLS2 is a variant of the PLS-R method where several Y-variables are modelled simultaneously. An advantage of this method is to find possible correlations or co-linearity between the Y-variables.

Malley et al. [8] developed prediction models for pH, total N, nitrate and nitrite, total C, organic C, C:N ratio, P, available P, S, K and Na by means of near infrared spectroscopy and PLS2. Suehara et al. [48] used PLS2 for simultaneous measurement of carbon and nitrogen content of composts using near infrared spectroscopy. Vergnoux et al. [21] applied PLS2 to predict physico-chemical (moisture, temperature, pH, NH4-N) and biochemical parameters (hemicellulose and cellulose) from NIR spectra.

Penalised signal regression (PSR)

This special regression method is described in Galvez-Sola et al. [49]. Galves Sola et al. [49] used this method to predict the phosphorus content in composts.
