因子分析案例

案例1：我國各地區(qū)財政支出的因子分析我國各地區(qū)主要財政支出工程包括一般公共效勞、國防、公共平安、教育、科學(xué)技術(shù)、文體傳媒、保障就業(yè)、醫(yī)療衛(wèi)生、環(huán)境保護(hù)、社區(qū)事務(wù)、農(nóng)林水事務(wù)、交通運(yùn)輸、其它支出等14項。根據(jù)2007年的數(shù)據(jù)，對這14個變量進(jìn)行分析，將它們綜合為少數(shù)幾個因子，通過對各地區(qū)的每個因子得分的分析了解各地區(qū)財政支出情況，為更合理地安排財政支出提供依據(jù)。1.首先利用主成分確定因子載荷矩陣。運(yùn)用spss輸出結(jié)果：1.1單變量描述統(tǒng)計：DescriptiveStatisticsMeanStd.DeviationAnalysisN一般公共效勞2049700.971177234.15631國防23415.4215255.05231公共平安928492.48657886.62131教育2170018.871303120.83031科學(xué)技術(shù)276916.23308520.69931文體傳媒248846.81137087.27831保障就業(yè)1646622.45896001.73231醫(yī)療衛(wèi)生630886.19330272.79331環(huán)境保護(hù)310076.68167762.45131社區(qū)事務(wù)1044674.74900747.96831農(nóng)林水事務(wù)997098.74455386.32831交通運(yùn)輸365524.84173055.00031工商金融等908076.42608414.48631其它支出766679.87983106.165311.2相關(guān)系數(shù)矩陣及顯著性水平檢驗(yàn)：一般公共效勞國防公共平安教育科學(xué)技術(shù)文體傳媒保障就業(yè)醫(yī)療衛(wèi)生環(huán)境保護(hù)社區(qū)事務(wù)農(nóng)林水事務(wù)交通運(yùn)輸工商金融等其它支出一般公共效勞1.00.774.907.969.626.792.714.877.512.650.912.615.644.618國防.7741.00.785.740.539.576.607.691.216.469.703.564.439.507公共平安.907.7851.00.948.847.852.641.907.273.738.761.497.649.841教育.969.740.9481.00.760.873.685.936.417.757.858.545.730.714科學(xué)技術(shù).626.539.847.7601.00.877.491.808.044.852.440.200.709.885文體傳媒.792.576.852.873.8771.00.579.922.360.813.708.414.743.696保障就業(yè).714.607.641.685.491.5791.00.674.561.603.694.363.758.489醫(yī)療衛(wèi)生.877.691.907.936.808.922.6741.00.432.721.835.565.713.709環(huán)境保護(hù).512.216.273.417.044.360.561.4321.00.195.650.631.343-.007社區(qū)事務(wù).650.469.738.757.852.813.603.721.1951.00.482.206.861.709農(nóng)林水事務(wù).912.703.761.858.440.708.694.835.650.4821.00.775.562.393交通運(yùn)輸.615.564.497.545.200.414.363.565.631.206.7751.00.248.199工商金融等.644.439.649.730.709.743.758.713.343.861.562.2481.00.576其它支出.618.507.841.714.885.696.489.709-.007.709.393.199.5761.00一般公共效勞.000.000.000.000.000.000.000.002.000.000.000.000.000國防.000.000.000.001.000.000.000.122.004.000.000.007.002公共平安.000.000.000.000.000.000.000.069.000.000.002.000.000教育.000.000.000.000.000.000.000.010.000.000.001.000.000科學(xué)技術(shù).000.001.000.000.000.003.000.407.000.007.141.000.000文體傳媒.000.000.000.000.000.000.000.023.000.000.010.000.000保障就業(yè).000.000.000.000.003.000.000.001.000.000.022.000.003醫(yī)療衛(wèi)生.000.000.000.000.000.000.000.008.000.000.000.000.000環(huán)境保護(hù).002.122.069.010.407.023.001.008.146.000.000.030.486社區(qū)事務(wù).000.004.000.000.000.000.000.000.146.003.133.000.000農(nóng)林水事務(wù).000.000.000.000.007.000.000.000.000.003.000.001.014交通運(yùn)輸.000.000.002.001.141.010.022.000.000.133.000.089.141工商金融等.000.007.000.000.000.000.000.000.030.000.001.089.000其它支出.000.002.000.000.000.000.003.000.486.000.014.141.0001.3KMO與Bartlett球形檢驗(yàn)〔檢驗(yàn)是否適合做因子分析〕：KMOandBartlett'sTestKaiser-Meyer-OlkinMeasureofSamplingAdequacy..788Bartlett'sTestofSphericityApprox.Chi-Square678.523df91Sig..0001.4變量共同度〔給出該次分析從每個原始變量中提取的信息〕：CommunalitiesInitialExtraction一般公共效勞1.000.925國防1.000.759公共平安1.000.972教育1.000.949科學(xué)技術(shù)1.000.939文體傳媒1.000.856保障就業(yè)1.000.760醫(yī)療衛(wèi)生1.000.917環(huán)境保護(hù)1.000.884社區(qū)事務(wù)1.000.885農(nóng)林水事務(wù)1.000.942交通運(yùn)輸1.000.814工商金融等1.000.898其它支出1.000.834ExtractionMethod:PrincipalComponentAnalysis.1.5方差解釋表〔顯示各主成分包含了各個原始變量總方差的情況〕TotalVarianceExplainedComponentInitialEigenvaluesExtractionSumsofSquaredLoadingsTotal%ofVarianceCumulative%Total%ofVarianceCumulative%19.42467.31167.3119.42467.31167.31121.95913.99681.3071.95913.99681.3073.9496.77688.083.9496.77688.0834.5563.97092.0535.3232.30694.3596.2922.08596.4447.1911.36697.8108.1491.06898.8779.066.47499.35110.039.27899.62911.024.16999.79712.015.10999.90713.009.06299.96814.004.032100.000ExtractionMethod:PrincipalComponentAnalysis.1.6碎石圖1.7主成分矩陣〔給出標(biāo)準(zhǔn)化原始變量用求得得主成分線性表示的近似表達(dá)式〕ComponentMatrixaComponent123一般公共效勞.935.195-.107國防.761.135-.402公共平安.950-.124-.232教育.971.019-.080科學(xué)技術(shù).821-.513-.043文體傳媒.909-.162.050保障就業(yè).771.157.375醫(yī)療衛(wèi)生.956.008-.056環(huán)境保護(hù).458.714.406社區(qū)事務(wù).811-.389.275農(nóng)林水事務(wù).850.465-.063交通運(yùn)輸.573.648-.257工商金融等.795-.198.477其它支出.754-.488-.170ExtractionMethod:PrincipalComponentAnalysis.a.3componentsextracted.標(biāo)準(zhǔn)的一般公共效勞=0.935*f1+0.195*f2-0.107*f3+e1……1.8因子得分系數(shù)矩陣〔用標(biāo)準(zhǔn)化原始變量表示標(biāo)準(zhǔn)化公共因子〕ComponentScoreCoefficientMatrixComponent123一般公共效勞.099.099-.113國防.081.069-.424公共平安.101-.063-.245教育.103.010-.084科學(xué)技術(shù).087-.262-.046文體傳媒.096-.083.053保障就業(yè).082.080.396醫(yī)療衛(wèi)生.101.004-.059環(huán)境保護(hù).049.364.428社區(qū)事務(wù).086-.199.290農(nóng)林水事務(wù).090.237-.067交通運(yùn)輸.061.330-.271工商金融等.084-.101.502其它支出.080-.249-.179ExtractionMethod:PrincipalComponentAnalysis.F1=0.099*標(biāo)準(zhǔn)化的一般公共效勞+0.081*標(biāo)準(zhǔn)化的國防+……+0.080*標(biāo)準(zhǔn)化的其他支出……1.9因子得分協(xié)方差矩陣〔單位陣，說明提取的公共因子不相關(guān)〕ComponentScoreCovarianceMatrixComponent12311.000.000.0002.0001.000.0003.000.0001.000ExtractionMethod:PrincipalComponentAnalysis.2.為尋找意義更明確、實(shí)際意義更明顯的公共因子，對初始公共因子進(jìn)行旋轉(zhuǎn)。Spss輸出結(jié)果：2.1旋轉(zhuǎn)后的因子載荷矩陣RotatedComponentMatrixaComponent123一般公共效勞.555.704.348國防.417.764.035公共平安.752.633.077教育.699.618.280科學(xué)技術(shù).937.241-.049文體傳媒.791.408.252保障就業(yè).533.279.631醫(yī)療衛(wèi)生.699.589.286環(huán)境保護(hù)-.055.359.867社區(qū)事務(wù).900.091.256農(nóng)林水事務(wù).323.762.507交通運(yùn)輸-.032.821.373工商金融等.797.048.511其它支出.851.297-.152ExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization.a.Rotationconvergedin17iterations.忽略特殊因子，可得：標(biāo)準(zhǔn)化一般公共效勞=0.555*f1+0.704*f2+0.348*f3……F1：科教文衛(wèi)因子；f2：根底效勞因子；f3：保護(hù)因子2.2因子得分系數(shù)矩陣〔可得到標(biāo)準(zhǔn)因子得分函數(shù)〕ComponentScoreCoefficientMatrixComponent123一般公共效勞-.008.180.006國防-.052.355-.249公共平安.077.184-.185教育.057.118-.022科學(xué)技術(shù).227-.052-.155文體傳媒.134-.021.025保障就業(yè).072-.168.369醫(yī)療衛(wèi)生.063.099-.008環(huán)境保護(hù)-.131-.066.545社區(qū)事務(wù).239-.238.132農(nóng)林水事務(wù)-.097.214.117交通運(yùn)輸-.211.376.008工商金融等.208-.327.345其它支出.192.036-.249ExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization.ComponentScores.F1=-0.008*標(biāo)準(zhǔn)化的一般公共效勞-0.052*標(biāo)準(zhǔn)化的國防+……+0.192*標(biāo)準(zhǔn)化的其他支出……利用標(biāo)準(zhǔn)化的因子得分函數(shù)，可計算各地區(qū)在不同因子上的得分，進(jìn)而進(jìn)行如排名等其他分析。地區(qū)f1排名地區(qū)f2排名地區(qū)f3排名上海3.267181廣東2.677641河南1.927451廣東2.405682江蘇1.612182四川1.913132北京1.424653四川1.416643內(nèi)蒙古1.376143山東1.370294浙江1.197494黑龍江1.075894江蘇0.99465云南1.126495山東0.875095浙江0.764566湖南0.669916江蘇0.820736遼寧0.653897廣西0.61357安徽0.715037天津0.330778貴州0.470218遼寧0.711258河南0.152719陜西0.204599陜西0.648279河北0.0052310福建0.1569810上海0.6264310湖北-0.063311河北0.1518511山西0.5736211福建-0.0890312新疆0.0887212河北0.546312吉林-0.2245413安徽0.0324813吉林0.4370313安徽-0.2830214河南0.0324314重慶0.24914黑龍江-0.337915山東0.023415湖北0.239215湖南-0.3436916遼寧0.0102316湖南0.1358616江西-0.3862217江西-0.0449817甘肅0.045317山西-0.3875918湖北-0.1118618云南-0.1092118廣西-0.4205819北京-0.1648219北京-0.4592819新疆-0.5839220內(nèi)蒙古-0.1790320新疆-0.5265620海南-0.5979521黑龍江-0.2330621貴州-0.5381921寧夏-0.6182922西藏-0.2442322江西-0.5411822重慶-0.6523723山西-0.297823浙江-0.5464323內(nèi)蒙古-0.7072724甘肅-0.4473624青海-0.7801324四川-0.713825重慶-0.5190525廣西-0.9710725陜西-0.7537726吉林-0.8615526天津-1.0476826甘肅-0.761127青海-1.0096427寧夏-1.0792427青海-0.7876228海南-1.0446928海南-1.4103528云南-0.8220929寧夏-1.1961929福建-1.4271829貴州-0.8908430天津-1.4270330西藏-1.5492730西藏-0.9447131上海-2.7034431廣東-1.9299631說明科教文衛(wèi)因子得分與該省經(jīng)濟(jì)水平有關(guān)，河北省接近全國平均水平；效勞支出與農(nóng)業(yè)有關(guān)，故沿海及農(nóng)業(yè)大省該項得分較高；河南、四川等省在保護(hù)支出得分較高，說明他們在環(huán)境保護(hù)、社會保障方面支出較多。利用方差奉獻(xiàn)率作為權(quán)重，乘以相應(yīng)因子得分，可計算綜合得分，進(jìn)而得到綜合排名：地區(qū)綜合得分排名廣東-0.137511上海0.9047572山東-0.134663江蘇-0.571854北京1.8632765浙江-0.263036遼寧-0.570297河南-0.644278河北0.0617919湖北0.23793410天津-0.1871611湖南-0.0420612福建-0.1283713安徽-0.2421114四川0.95072915黑龍江-0.3029316吉林0.48976617廣西-0.4078818山西-0.6567319江西-0.7243320云南0.98492721內(nèi)蒙古-0.263722新疆-0.4348123陜西1.86324524重慶-0.1525625貴州-0.0480726甘肅-0.7750527海南-0.416328寧夏-0.4030929青海0.64520830西藏-0.4948931可見，支出與該省市的經(jīng)濟(jì)實(shí)力有關(guān)，經(jīng)濟(jì)實(shí)力越強(qiáng)，支出越多，反之那么越少。案例2中心城市的重要開展是帶動周邊地區(qū)經(jīng)濟(jì)開展的重要動力。在我國經(jīng)濟(jì)開展進(jìn)程中，各個中心城市一直是該地區(qū)經(jīng)濟(jì)和社會開展的“引路者〞。因而，分析評價全國35各中心城市的綜合開展水平，無論是對城市自身的開展，還是對周邊地區(qū)的進(jìn)步，都具有十分重要的意義。下表是城市綜合開展水平的12項指標(biāo)，試對全國35各中心城市的綜合開展水平做分析評價。x1x2x3x4x5x6北京830.83810363030671.14127.4592538864413910天津549.74404961033467915.38204529518253200石家莊331.331198150510008.488.0749342910444919太原222.63518320015248.112.433334736601300呼和浩特97.8124077944155.122057792554496沈陽440.61064361214635.747.381088914229575長春313.051511527010891.986.944597098313564哈爾濱454.5272150899517.824.9976360011536951上海1041.391.03E+086386135.22899285060546000南京391.672509381614804.687.62136478811336202杭州263.673202522616815.28.36150388814664200合肥160.1853486054640.843.393586943592488福州205.43128895738250.394.696745228762245南昌195.4641491694454.453.623140944828029濟(jì)南297.211318542514354.46.67610547583525鄭州249.7292704947846.918.7765873710484859武漢474.981334493816610.3413.5880436812855341長沙205.83533930410630.56.315989307048500廣州493.324017832428859.4521.47274770737273276南寧167.9920837635893.094.953624354514961?？?6.0520256433304.42.721225412843664成都386.23970097628798.28.0689575214944197貴陽165.2735694195317.555.754038553449487昆明205.34580957312337.867.076011017085278西安312.886386627939212.2164803712105607蘭州175.5452154905580.83.72056604683830西寧105.1311489592037.151.24843971749293銀川79.214648672127.171.651226051930771烏魯木齊142.94311094312754.023.944091194203000大連297.481546864121081.476.6110540513101986寧波168.812630286213797.384.8139416210596339廈門83.74132023003054.822.837014563971559青島329.962558869530552.66.7212023989084693深圳122.39524510376792.6610.84290837021994500重慶753.921588992832450.212.83161561818965569x7x8x9x10x11x12北京434.15109893651517.38.5644.94天津174.53254148187.997.2317.45石家莊86.741067432187.238.2821.56太原74.55945212165.067.8820.58呼和浩特28.9407963183.818.9