PLS Introduction to SIMCA-P and Its Application

Chapter 32Introduction to SIMCA-P and Its Application

Abstract SIMCA-P is a kind of user-friendly software developed by Umetrics,which is mainly used for the methods of principle component analysis (PCA) andpartial least square (PLS) regression. This paper introduces the main glossaries,analysis cycle and basic operations in SIMCA-P via a practical example. In theapplication section, this paper adopts SIMCA-P to estimate the PLS model withqualitative variables in independent variables set and applies it in the stand stormprevention in Beijing. Furthermore, this paper demonstrates the advantage of lower-ing the wind erosion by Conservation Tillage method and shows that ConservationTillage is worth promotion in Beijing sand storm prevention.

32.1 Introduction to SIMCA-P

32.1.1 About SIMCA-P Software

SIMCA-P is developed by Umetrics, which is mainly used for the methods of princi-ple component analysis (PCA) and partial least square (PLS) regression. It is a kindof user-friendly software based on Windows: the operations of models in SIMCA-Pare very convenient to handle and the results can be easily illustrated by plots andlists, which present the explanations of the models in kinds of forms. At present,

Z. Wu and H. WangSchool of Economics and Management, Beihang University, 37 Xueyuan Road, Haidian District,Beijing 100083, Chinae-mail: [email protected], [email protected]

D. LiAgricultural Bank of China, Beijing 100036, Chinae-mail: [email protected]

School of Statistics, Central University of Finance and Economics, Beijing 100081, Chinae-mail: [email protected]

V. Esposito Vinzi et al. (eds.), Handbook of Partial Least Squares, Springer Handbooksof Computational Statistics, DOI 10.1007/978-3-540-32827-8 33,c� Springer-Verlag Berlin Heidelberg 2010

757

Zaibin Wu, Dapeng Li, Jie Meng, and Huiwen Wang

J. Meng

[email protected]

[email protected]

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SIMCA-P has been a standard tool in PLS regression analysis for researchers inmany fields of science and technology.

32.1.2 Some Glossaries in SIMCA-P

There are several special glossaries in SIMCA-P system, which would help us togain a mastery of the software.

(1) Project. SIMCA-P is organized into projects. A project is a folder including themodels with the relative statistics and results.

(2) List. All the data are listed in tables in the system. The first row with the variablenames is marked as the Primary variable ID. The first column is marked asidentification numbers.

(3) Dataset. The set of processing data is known as a Dataset. A project may containseveral datasets.

(4) Model. Models are mathematical representations of your process and are devel-oped using the data specified in the workset and with a specified model type.

(5) Workset. A workset is the set of data processed by the current active model.A workset can contain all the data, or be a subset of the primary data, witha particular treatment of the variables, such as role (predictor variables X, orresponses Y),scaling, transformation, lagging, etc.

(6) Block. A block is a combination of the variables with same role. For example,the Y block in a PLS model refers to all the dependent variables (responses).

(7) Class. The observations of a dataset can be spitted into different set for differentpurposes, known as class.

32.1.3 The Analysis Cycle

It is convenient to do PCA or PLS estimation with SIMCA-P. Users can get theanalysis results after several steps in accordance with the principles of PCA or PLSmethods. The analysis cycles can be summarized as follows.

(1) Start a project. Users should import the primary data form file or databases tocreate a new project.

(2) Preprocess the data. View or modify a SIMCA-P data set. For example, it is easyto generate new variables as functions of existing ones or from model results.Users can do similar operations to preprocess the data.

(3) Prepare the workset. The default workset is the whole data set with all variablesas X at the project start, and the default model (unfitted) is a principal componentmodel of X. Users should change the role of the variables to fit other models.

(4) Fit the models. After all the preparing procedures, users can do the estimation.(5) Detect the outliers. Display the score scatter plot to show the possible presence

of outliers, groups, and other patterns in the data. Users should exclude theoutliers from the workset and go back to step (4) to fit a new model.

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1. Start a projectImport data to

create a project

2. Preprocess the dataView or modify

a SIMCA-P dataset

3. Prepare the worksetChange the role of variable

and specify model type

4. Fit the modelFit the model

automatically or artificially

5. Detect outliersDetect outliers and exclude

them if existing

6. Review the fitJudge the effect and

interpretate the results

7. To do predictionSpecify a datasetto do prediction

Fig. 32.1 Road map to SIMCA-P

(6) Review the fit. After a fit, the whole spectrum of plots and lists are availablefor model interpretation. Users should judge the effect of the fitted model anddecide whether to do prediction.

(7) To do prediction. Build the prediction set from the primary or any secondarydata sets to do prediction.

The above steps can be shown as the above road map (Fig. 32.1).

32.2 The Basic Operations of SIMCA-P

The example below will illustrate the main operations of SIMCA-P. The data inthis example describes the relationship between body condition and sports gradeof people. The predictors reflect one’s body condition including avoirdupois, cum-merbund and pulse. The responses are three grades of physical exercise includingchin-up, curl and high jump. 20 persons have been selected. Table 32.1 shows theoriginal data set (Jone Neter, used by Tenenhaus 1998).

32.2.1 The Main Window of SIMCA-P

Double click on the SIMCA-P icon on the desktop, the main window opens anddisplays as Fig. 32.2. (Note: Before this operation, the project with the above datain Table 32.1 has been created. Otherwise the active model status window will notdisplay.)

The main window includes the following parts.

(1) The command menu bar. The name and the folder of a project will be shown inthe title. The menu in the bar includes the entire functions menu.

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Table 32.1 Observed data of body condition and sports grade

No avoirdupois cummerbund pulse chin-up curl high jump

1 191 36 50 5 162 602 189 37 52 2 110 603 193 38 58 12 101 1014 162 35 62 12 105 375 189 35 46 13 155 586 182 32 56 4 101 427 211 38 56 8 101 388 167 34 60 6 125 409 176 31 74 15 200 40

10 154 33 56 17 251 25011 169 34 50 17 120 3812 166 33 52 13 210 11513 154 34 64 14 215 10514 247 46 50 1 50 5015 193 36 46 6 70 3116 202 37 62 12 210 12017 176 37 54 4 60 2518 157 32 52 11 230 8019 156 33 54 15 225 7320 138 33 68 2 110 43

Fig. 32.2 Main window of SIMCA-P


(2) Standard and shortcut bar. These shortcut buttons are for activating commandmenus and plots. Pressing a button will perform a certain task.

(3) Plot and maker bar. Use the buttons in Plot toolbar to insert labels or text inplot, enlarge and read positions in graphs, get information about observations orvariables, show a regression line in scatter plots or rotate 3D graphs. The mainfunction of Maker toolbar is to exclude or include the observations or variablesin the active model and create a new model.

(4) The Favorites window. The Favorites window contains commands and plots,which are marked with different symbols. Double click on a symbol will executea command or open a specified plot.

(5) The Workset bar. The bar displays the variables and observations in the worksetand their status.

(6) The active model status window. The window shows the information about allthe models, such as model name, type, number of components, etc.

(7) The Audit Trail window. The log events are shown in this window.

32.2.2 The Operations of SIMCA-P

The important operations are as followings.(1) Import the data and create a projectData can only be imported from file or data bases, but not by keyboard. The

system supports more than 10 types of files, such as txt, xls, mat, etc. SelectFilejNewjGet data from file, a standard dialog box opens to enter the file type, nameand source address of the data file to be imported (Fig. 32.3).

After importing the data file, the first page of the import wizard opens (Fig. 32.4).The row with the variable names is by default marked as the Primary variable IDand colored in dark green. You can select any other row as the Primary variableID. If the Primary variable ID has not been specified, SIMCA-P creates the Primaryvariable ID as Var 1, Var 2, etc. The column with observation numbers or names iscolored in dark yellow. Select any desired column as Primary Observation ID. Dataare colored in white and text are colored in blue.

Fig. 32.3 Import the data file

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Fig. 32.4 Import data wizard

Fig. 32.5 Specification of the project

Fig. 32.6 The active model status window

In the Import data wizard, you can do other operations by pressing the buttonson the left window.

Click on Next, the project specification page of the import wizard displays(Fig. 32.5). Users should specify the project name and the folder to save the workfile. The file type is usp. The window still displays other information about thedata set.

Click on Finish and the data set is imported. A project has been created(Fig. 32.6). The default workset is the whole data set with all variables as X andscaled to unit variance. The associated model is PCA.

(2) Explore the dataBefore fitting the model, you should understand the data comprehensively. Select

DatasetjQuick infojVariables/Observations, a window opens with the name of the


Fig. 32.7 Usual statistics and dataset

Fig. 32.8 Generate variables

variable/observation and default options (Fig. 32.7). The usual statistics are showedin the window, such as number, missing values, mean, etc.

In some case, a new variable should be generated from raw data. Select DatasetjGenerate Variable, SIMCA-P opens the wizard window displaying the active dataset in a spreadsheet (Fig. 32.8).

Enter the expression defining the new variable and click on Next. SIMCA-P dis-plays the new variable, with its formula, statistics and Quick info plots (Fig. 32.9).

Click finish, and the new variable is added at the end of the active dataset.(3) Create the workset and set model optionsAfter the primary data set is loaded, all the variables are selected as X variables

(predictors). The active model type is PCX (Principle Component Analysis of the Xvariables).

In order to change the role of the variables or observations, you can selectWorksetjEdit to open the Overview page of the workset dialog with the currentobservations and variables and their attributes (Fig. 32.10).

The workset is organized into pages. Select the desired page to change theattributes of the observations or variables. In order to do PLS estimation, you canselect WorksetjEdit to change roles of variables by marking the variable y and

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Fig. 32.9 Info of new variable

Fig. 32.10 Overview page of the workset dialog

Fig. 32.11 Specify variables as responses

clicking on the desired button Y (Fig. 32.11). You can also set class of observationsin the Observations page.

After the above procedures, you can select WorksetjOptions to set the options ofthe current active model (Fig. 32.12).

(4) Fit the modelYou can select Analysis menu to fit the model. The model is by default non hier-

archical base model. The model type is decided according to the role of variables,including PCA on X-block, PCA on Y-block, etc. The methods of fit include autofit,


Fig. 32.12 Model options

Fig. 32.13 Fit the model

Fig. 32.14 Model overview

next component, 2 first components, next component, zero component, removecomponent and autofit class models (Fig. 32.13).

Select AnalysisjAutofit, SIMCA-P extracts as many components as consideredsignificant. When you fit a model, a plot window opens and displays the cumulativeR2 and Q2 for the X(PCA) or Y(PLS) matrix (Fig. 32.14).

After fitting a model, you can mark the model and click on Active ModelTypejHierarchical Base Model and select scores, residuals, or both as variables in

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Fig. 32.15 Hieraarchical base model

Fig. 32.16 t[1]/t[2] scatter plot

another model (Fig. 32.15). The scores, residuals, or both would be added to theworkset to be used as variables in another model.

(5) Detect the outliersDouble click t[1]/t[2] Scatter Plot in Favorite window to display score scatter

plot after fitting (Fig. 32.16). These plots show the possible presence of outliers,groups, and other patterns in the data. In order to illustrate this plot, we extract twocomponents.

In Fig. 32.16, observation 14 is outside the 95% confidence region of the model.This means observation 14 is an outlier. In order to eliminate the effect of obser-vation 14, you should exclude this observation from the workset. Press Mark itembutton in Marker toolbar and mark observation 14, and then press the red arrow but-ton. Resultingly, observation 14 is excluded from workset and a new unfitted modelis created without observation 14 (Fig. 32.17).

(6) Review the resultsYou can select Analysis to plot or list some statistics, including scores, loading,

coefficients, etc. For example, you can select AnalysisjSummaryjList to show theindividual cumulative R2 and Q2 for each Y variable (Fig. 32.18).

In fact, you can double click a ceratin symbol in Favorites window to executea command. The Favorites bar is similar to a customized Navigation Bar. It con-tains commands and plots. They are marked with different symbols for specified


Fig. 32.17 Detect the outliers

Fig. 32.18 Summary of the results

Fig. 32.19 Coefficients Plot

plots/lists and for a command (works on the active model). For example, you candouble click on the Coefficients Plot in Favorites window to show the coefficientsplot (Fig. 32.19).

Besides the results included in Analysis menu and Favorites window, you canalso select Plot/List menu to plot or list all the results. The Plot/List menus allowyou to plot and list input data such as observations and variable values, compute

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elements such as scaling weights, variable variances, etc., as well as results such asloadings, scores, predictions, etc., of all the fitted models.

(7) To do PredictionAfter fitting, the workset is by default specified as prediction set. If you want

to build a prediction set by combining observations from different data sets, orremoves observations from the prediction set, select PredictionsjSpecify PredictionsSetjSpecify.

The observations are displayed in the left window (Fig. 32.20). Select the onesyou want in the prediction set and move them to the right window.

After specifying the prediction set, you can select Predictions menu to obtainthe prediction information about the current model. For example, you can selectDistance to ModeljY BlockjLine Plot to display this plot (Fig. 32.21).

The residual standard deviation of an observation in the Y space is proportional tothe observation distance to the hyper plane of the PLS model in the correspondingspace. SIMCA-P computes the observation distances to the PLS model in the Y

Fig. 32.20 Specify predictions set

Fig. 32.21 Distance to model


space (DModY) and displays them as line plots. A large DModY value indicatesthat the observation is an outlier in the Y space. By default, these distances arecomputed after all extracted components.

32.3 Application

In this section, we provide an application of SIMCA-P. Sandstorms have been abig barrier against the development of the world, which results in an annual globalloss of 48 billion USD, including 6.5 billion USD in China. In recent years, sandstorms in Beijing have caused many serious problems. Investigations showed thatabout 70 percent of the sand in these storms are generated by wind erosion ofdry, fallow farmland around the city. Consequently, the study on wind erosion ofsoil becomes very important in sand storm prevention (Shen et al. 2000; Li andGao 2001; Gao 2002; Zang 2003).

In this research, the Water Content in Soil .x1/, Soil Particle Size.x2/,the Rate ofStraw Mulching .x3/ and the Type of Farmland is defined as four independent vari-ables (IVs). The Type of Farmland is a qualitative variable (QV) consisting of thefollowing four categories: sand farmland, traditional tillage farmland, grass farm-land and Conservation Tillage farmland. These categories are regarded as differenttypes of farmland. To establish a regression model of Wind Erosion Rate .y/with theabove four IVs, the Type of Farmland should be transformed into four dummy vari-ables (DVs), D1; D2; D3; D4. Table 32.2 shows the original data set. The samplesize is 16.

Based on the data in Table 32.2, the regression model can be written as follows:

y D u C ˇ1x1 C ˇ2x2 C ˇ3x3 C ˛1D1 C ˛2D2 C ˛3D3 C ˛4D4 (32.1)

Table 32.2 Wind erosion rate and IVsNo y x1 x2 x3 D1 D2 D3 D4

1 11:674 3:623 0:651 12.4 1 0 0 02 13:812 3:623 0:651 12.4 1 0 0 03 15:260 3:623 0:651 12.4 1 0 0 04 12:160 3:623 0:651 12.4 1 0 0 05 6:021 6:291 0:266 13.8 0 1 0 06 8:598 6:291 0:266 13.8 0 1 0 07 10:395 6:291 0:266 13.8 0 1 0 08 7:331 6:291 0:266 13.8 0 1 0 09 3:689 10:210 0:337 45.4 0 0 1 010 5:339 10:210 0:337 45.4 0 0 1 011 5:971 10:210 0:337 45.4 0 0 1 012 4:893 10:210 0:337 45.4 0 0 1 013 2:768 8:883 0:339 58.5 0 0 0 114 4:167 8:883 0:339 58.5 0 0 0 115 4:357 8:883 0:339 58.5 0 0 0 116 4:111 8:883 0:339 58.5 0 0 0 1

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Fig. 32.22 Get the data from file

Fig. 32.23 Import data

It is clear that the following equation always exists in the model (1):

D1 C D2 C D3 C D4 D 1 (32.2)

The above results show that there is full multicollinearity between the IVs. Wehave used SAS 8.0 to obtain the estimation. The system provides the followingnotes: the model is not of full rank; the least-squares solutions for the parametersare not unique; some statistics will be misleading. A reported DF of 0 or B meansthat the estimate is biased. Therefore, OLS method is invalid in this case study.

Consequently, we adopted PLS to establish the regression model, which wasexecuted by SIMCA-P 9.0.

At the beginning, select FilejNewjGet data from file to import the primary datasetand create a new project (Fig. 32.22).

The raw data was stored in c:n and the name of the source file is sand.dif. Afterthe file was selected, the window of Import data wizard was displayed (Fig. 32.23).

The first row with the variable names is by default marked as the Primary variableID. The first column is by default marked as identification numbers.Click on Nextin Import data wizard when finished.

After importing the data, we should specify the project name and select thedestination folder to save the project (Fig. 32.24).

After the above procedures, a project has been created. By default all variablesare selected as X. The active model type is PCX (Fig. 32.25).

In order to adopt PLS estimation, we can select WorksetjEdit to change all theoptions of the default model in Workset Window. Variables are displayed with theirroles (X, Y or excluded (�)). To change roles, mark the variable y and click on thedesired button Y (Fig. 32.26).


Fig. 32.24 Specification of the project

Fig. 32.25 The default model

Fig. 32.26 Change the role of variable y

Fig. 32.27 Change the role of variable y

When we exit the Workset window, the model type has been changed from PCXto PLS. This model is unfitted and is the active model (Fig. 32.27).

SIMCA-P extracts one component according to the cross validation rules afterselecting AnalysisjAutofit. The right plot displays the cumulative R2 and Q2 for theY (PLS) matrix after the extracted component (Fig. 32.28).

Double click t[1]/u[1] Scatter Plot in Favorites window to display the t1=u1 plot(Fig. 32.29).

The plot indicates a good fit corresponding to the small scatter around the straightline. It proves that there is a strong linear correlation between Wind Erosion Rateand its IVs. So the linear regression is fundamentally established.

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Fig. 32.28 The PLS model

Fig. 32.29 t[1]/u[1] scatter plot

Fig. 32.30 t[1]/t[2] scatter plot

For a better illustration of the regression results, we extracted two components.The cumulative Q2 for the extracted components is 0.848 and it can explain 72.6%variation of IVs and 90.2% variation of y.

Double click t[1]/t[2] Scatter Plot in Favorites window to display a two-dimen-sional score plot (Fig. 32.30).

SIMCA-P draws the confidence ellipse based on Hotelling T2. Observationssituated outside the ellipse are outliers. Figure 32.30 shows no outliers.

Double click Observed vs. Predicted in Favorites window to shows the observedvalues vs. the fitted or predicted values (Fig. 32.31).


Fig. 32.31 Observed vs. Predicted values

Fig. 32.32 Standardized regression coefficients

Figure 32.31 demonstrates that the estimation by PLS is effective. The modelconsisting of original variables is estimated as follows:

y D 9:36 � 0:36x1 C 5:54x2 � 0:03x3 C 2:11D1 C 0:10D2 � 0:59D3 � 1:62D4

(32.3)Double click Coefficients Plot in Favorites window to show standardized regres-

sion coefficients of the model (Fig. 32.32).According to Fig. 32.32, the larger the size of soil particle, the more serious the

wind erosion. Furthermore, because Soil Water Content and Straw Mulching Rateare negatively correlated with Wind Erosion Rate, these are beneficial in easing thesoil wind erosion problem by adding Soil Water Content and increasing the StrawMulching Rate. Considering the different kinds of farmland, we conclude that theConservation Tillage farmland has the lowest wind erosion rate, while the Sandfarmland has the highest.

Double click w*c[1]/w*c[2] Scatter Plot in Favorites window to show both the X-weights (w or w*) and Y-weights (c) and thereby the correlation structure betweenX and Y (Fig. 32.33).

Since the Conservation Tillage method cultivates the farmland in a shallow wayand leaves the crop residues on the land surface as much as possible, it is the mosteffective way to prevent wind erosion. Additionally, it can increase land coverage

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Fig. 32.33 Loading plots of IVs

rate, prevent water and soil loss and enlarge the level of production. Therefore, it isworthwhile promoting the Conservation Tillage method both for the prevention ofsand storms in the Beijing area and for agricultural production.

32.4 Conclusion

This paper has introduced fitting modes by employing SIMCA-P. It is obvious thatSIMCA-P is an effective tool to conduct multivariate data analysis. In the part ofempirical research, the results show that, compared with OLS, PLS is preferable indealing with QVs. In the investigation, the PLS model not only illustrated the factorsof soil wind erosion, which conformed fairly well with reality, but also demonstratedthat Conservation Tillage method is the most effective way to ease soil wind erosion.The results provide valuable information for Beijing sand storm prevention.

References

UMETRI AB: SIMCA-P for Windows: Maltivariate Modeling, Analysis and SPC of Process Data.UMETRI AB (1996)

Tenenhaus, M.: La Rgression PLS: Thorie et Pratique. TECHNIP, Paris (1998)Shen, Y.C., Yang, Q.Y., Jing, K, Xu, J.X.: Sand-storm and Dust-storm in China and Prevention and

Control. Journal of Arid Land Resources and Environment, 14(3), 11–14 (2000)Li, L.J., Gao, Q.X.: Source Analysis of Beijing Sand-Dust in 2000, Research of Environmental

Sciences, 14(2), 1–4 (2001)Gao, Q.X.: The Dust Weather of Beijing and Its Impact, China Environmental Science, 22(5),

468–471 (2002)Zang, Y.: Experimental Study on Soil Erosion by Wind under Conservation Tillage, 19(2), 56–60

(2003)

PLS Introduction to SIMCA-P and Its Application

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