4.4 Mactor Analysis and Principal Component Analys...
Two research methods are introduced in this section：factor analysis and principal com ponent analysis.Both can be seen as approaches to reduce the com plexity of data.Principal components“aim to produce a small number of derived variables that can be used in place of the larger number of original variables to sim plify subsequent analysis of the data”（Landau＆Everitt 2003：283）.Factor analysis，unlike principal component analysis，beginswith a hypothesis about the covariance（or correlational）structure of the variables.“It is concerned with whether the covariances or correlations between a set of observed variables can be explained in terms of a smaller number of unobservable constructs known either as latent variables or common factors”（Landau＆Everitt 2003：288）.As for tourism texts analysis，the two methods are compounded together to present a better illustration.
On the basis of the former study，thirty-six variables are applied for further analysis，including STTR，W L，SL，HFW，LD，NOUN，NP，ADJ，VERB，LADV，CW，FADV，DET，PREP，NUM，AUX，CONJ，PRON，THE，OF，AND，TO，IN，FOR，PREPW ITH，FROM，AS，AT，ON，PREPBY，IS，WAS，ARE，YOU，IT，THAT.
Table 4.11 Standardized Data for Factor Analysis[2]
The procedures for factor analysis and principal com ponent analysis are as follow s：
Step One：load the variables and statistics into SPSS 26.0.
Step Two：use the comm ands“Analyze-Data Reduction-Factor...”Display 4.3（1）to transform variables to principal components.First，add the thirty-six factors to the“variables”dialogue box；then select checkbox“initial solution”，“coeficients”，“KMO and Bartlett's test of sphericity”in sub-dialogue box“Descriptives”（2）and click“Continue”；click“Extraction”（3）and opt for principal com ponents in themethod list；at last，set“Suppress absolute values less than 0.7”in sub-Dialogue Box“Options”（4）to ensure values have significantmeaning for analysis.Click OK in Dialogue Box（1），then output of factor analysiswill be declared.（See Table 4.12）.
Display 4.3 Steps of Declaring Factor Analysis
Table 4.12 Output of Factor Analysis
“Total Variance Explained”shows how much of the total variance of the observed variables is explained by each of the principal components.Altogether，four principal components account for 100%of total variance.Nam ely，the thirty-six variables can be reduced to four classified com ponents.The first principal com ponent（scaled eigenvector），by definition the one that explains the largest part of the total variance has a variance（eigenvalue）of 15.74；this amounts to 43.7%of the total variance.The second principal com ponent has a variance of about10.1 and accounts for a further 28%of the variance and so on.The“Cumulative%”column of the table tells us how much of the total variance can be accounted for by the first kcomponents together.The first two principal com ponents account for 71.77%，the first three 90.86%of the total variance.
Then，let's come to“Com ponent Matrix”.The coefficients in this table specify the linear function of the observed variables that define each com ponent.The variableswith high coefficients，like SL（0.927），HFW（0.974），NOUN（0.91），ADJ（0.804），PREP（0.901），NUM（0.703），AUX（0.985），CONJ（0.774），PRON（0.737），IT（0.96）indicate they are salient on the first principal component.On the other side，STTR（－0.955），NP（－0.954），FADV（－0.91）are negatively salient.Similarly，AND，AT and ARE are positively，W Lnegatively salient on the second principal com ponent.On the third principal component，LADV and TO are positively salient，W ITH is negatively salient.On the fourth principal com ponent，THAT is positively salient
Step Three：calculate the coefficients for principal com ponent analysis by“Transform-Com pute variables...”with the formula“A1＝B1／SQR（eigenvector）”（Display 4.4）.B1 refers to the coefficients displayed in Table 4.12（including those less than 0.7）.Eigenvectors have been shown in the same table，15.738 for the first principal component.The new ly calculated coefficients are listed in Table 4.13.(https://www.daowen.com)
Table 4.13 Coefficient for Principal Component Analysis
The expression form ula can be written as follow s：
F1＝－0.241ZX1＋（－0.139）ZX2＋0.234ZX3＋...＋0.080ZX36
F2＝0.090ZX1＋（－0.250）ZX2＋0.058ZX3＋...＋（－0.047）ZX36
F3＝0.011ZX1＋0.072ZX2＋0.107ZX3＋...＋0.225ZX36
F4＝0.044ZX1＋0.096ZX2＋0.093ZX3＋...＋0.401ZX36
ZXn is standardized scores which can be requested in SPSS by“Analyze-Descriptives...”（Display 4.4）.Add X1～X36 as“Variables”，select the checkbox of“Save standardized values as variables”，and then the standardized values will be displayed automatically in SPSS data editor.
Display 4.4 Dialogue Box for Principal Component Analysis
Step Four：Interpret values of principal components.The descriptive data is arrayed in descending order in Table 4.14.
Table 4.14 Descriptive Statistics of Principal Com ponent Analysis
Observing the data，TETTC are salient on Component 1 and 4；TETTN on Com ponent 1 and 2；OETTC on Com ponent 3；OETTN on Com ponent 2 and 3.Overall，TETT is distinguishing on the use of SL，HFW，NOUN，ADJ，PREP，AUX，IT and THAT，exhibiting the features of long sentences，less words，over-description，exaggeration，thirdperson perspective.By contrast，OETT reflects the features of short sentences，diversified words and more adverbs.