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)主要財政支出項目包括普通公共服務(wù)、國防、公共安全、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)2022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)的每一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)。.首先利用主成份確定因子載荷矩陣。運(yùn)用spss輸出結(jié)果：MeanStd.Deviation_AnalvsisN_普通公共服務(wù)國防公共安全教育科學(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2049700.9723415.42928492.482170018.87276916.23248846.811646622.45630886.19310076.681044674.74997098.74365524.84908076.42766679.871177234.15615255.052657886.6211303120.830308520.699137087.278896001.732330272.793167762.451900747.968455386.328173055.000608414.486983106.1653131313131313131313131313131相關(guān)系數(shù)矩陣及顯著性水平檢驗:普通公共服務(wù)國防公共安全教育科學(xué)特不文體傳媒保障就業(yè)醫(yī)療衛(wèi)牛環(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普通公共服務(wù)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公共安全.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-.007.709.393.199.5761.00x7x8x9xlOxllxl2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28.9407963183.818.9226.58沈陽101.71521548159.326.728.36長春89.712441671511.877.0318.75哈爾濱168.8321021651412.756.3418.51上海281.5176865111914.5712.9219.11南京87.911950742169.0612.13136.72杭州75.721867776178.936.523.19合月巴37.885265771714.1115.7228.74福州71.31073262189.657.931.6南昌49.79692717177.377.6723.98濟(jì)南78.381256160197.7710.6219.54關(guān)B州83.9911370561910.117.6317.77武漢136.081868350176.874.168.34長沙60.0410199241810.099.129.1廣州182.1652470871711.1612.76178.76南寧50.79668976189.919.3235.12海口22.97340392205.097.0715.79成都124.031894496178.9510.1725.59貴陽54.53664234169.373.11105.35昆明73.3410454691515.334.4923.33西安113.731535896157.324.488.82蘭州54.917406611510.336.311.22西寧20.63013641711.474.9214.2銀川29.12393035159.2610.4340.21烏魯木齊47.427828731922.896.4920.53大連82.1314422151413.796.2440.21寧波59.881418635179.886.8117.65廈門54.7810421112015.58.1526.44青島104.5516033051514.7811.4135.78深圳104.98325990021114.9147.29177.62重慶203.792535070214.944.2410.8普通公共服務(wù)國防.000.000.000.000.000.000.000.001.000.000.000.000.000.000.002,122.000.004.000.000.000.000.000.007.000.002公共安全.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.000.002.000.000.000.000.003.000.486.000.014.141.000KMO與Bartlett球形檢驗（檢驗是否適合做因子分析）：KMOandBartlett'sTestKaiser-Meyer-OlkinMeasureofSamplingAdequacy.BartlettsTestofSphericity Approx.Chi-SquaredfSia..788678.52391.000變量共同度（給出該次分析從每一個原始變量中提取的信息）:CommunaIities InitialExtraction普通公共服務(wù)國防公共安全教育科學(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1.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.0001.000.925.759.972.949.939.856.760.917.884.885.942.814.898.834ExtractionMethod:PrincipalComponentAnalysis.方差解釋表（顯示各主成份包含了各個原始變量總方差的情況）TotalVarianceExplainedComoonentInitialEicanvahiasExtracionSumsofSolaredLoadinasTotal%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.碎石圖ScreePlot主成份矩陣（給出標(biāo)準(zhǔn)化原始變量用求得得主成份線性表示的近似表達(dá)式）ComnonentMatrixaComnnnpnt123普通公共服務(wù).935.195-.107國防.761.135-.402公共安全.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)的普通公共服務(wù)=0.935*f1+0.195*f2-0.107*f3+e1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）CompqpentScoreCoefficientMatrixComnonpnt123普通公共服務(wù).099.099-.113國防.081.069-.424公共安全.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.080-249-17QComoopentScoreCoefficientMatrixCnmnnnpnt123普通公共服務(wù).099.099-.113國防.081.069-.424公共安全.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.080-24Q-179ExtractionMethod:PrincipalComponentAnalysis.51=0.099*標(biāo)準(zhǔn)化的普通公共服務(wù)+0.081*標(biāo)準(zhǔn)化的國防+……+0.080*標(biāo)準(zhǔn)化的其他支出因子得分協(xié)方差矩陣（單位陣，說明提取的公共因子不相關(guān)）ComoonentScoreCovarianceMatrixComoonenL12311.000.000.0002.0001.000.0003.000.0001.000ExtractionMethod:PrincipalComponentAnalysis..為尋覓意義更明確、實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：旋轉(zhuǎn)后的因子載荷矩陣RotatedComDonentMatrixaComoonent123普通公共服務(wù).555.704.348國防.417.764.035公共安全.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.851.297-1^2ExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization,a.Rotationconvergedin17iterations.忽略特殊因子，可得：標(biāo)準(zhǔn)化普通公共月艮務(wù)=0.555*f1+0,704*f2+0,348葉3F1：科教文衛(wèi)因子；f2：基礎(chǔ)服務(wù)因子；f3：保護(hù)因子因子得分系數(shù)矩陣（可得到標(biāo)準(zhǔn)因子得分函數(shù)）ComDonentScoreCoefficientMatrixComnonRnt123普通公共服務(wù)國防公共安全教育科學(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-.008-.052.077.072.063-.131.239-.097-.80.355.184.118-.052-.021-.168.099-.066-.238.214.376-.327.036.006-.249-.185-.022-.155.025.369-.008.508.345-24QExtractionMethod:PrincipalComponentAnalysis.RotationMethod:VarimaxwithKaiserNormalization.ComponentScores.+0.192*標(biāo)準(zhǔn)化的F1=-0.008/標(biāo)準(zhǔn)化的普通公共服務(wù)-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)fl排名地區(qū)1f2排名地區(qū)f3排名上海3.26718廣東2.67764.河南1.927451廣東2.40568江蘇1.61218四川1.913132北京1.424653四川1.416643內(nèi)蒙古1.376143山東1.3702S4浙江1.1974S4黑龍江1.075894江蘇0.9946E云南1.126495山東0.875095浙江0.764566湖南0.669936江蘇0.820736遼寧0.653897廣西0.61357安徽0.715037天津0.3307/8貴州0.470218遼寧0.711258*I南0.152710陜西0.2045SC陜西0.648279河北0.005231C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-0.34369ie遼寧0.0102316湖南0.1358616江西-0.3862217江西-0.0449817甘肅0.045317山西-0.387591￡湖北-0.1118618右南-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)家古-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-1.0476826廿肅-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-0.890843C天津-1.4270330西藏-1.5492730西藏-0.944713；上海-2.7034431廣東-1.9299631說明1.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；2.服務(wù)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；3.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。利用方差貢獻(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-0.0480726廿肅-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)實力有關(guān)，經(jīng)濟(jì)實力越強(qiáng)，支出越多，反之則越少。案例2中心城市的重要發(fā)展是帶動周邊地區(qū)經(jīng)濟(jì)發(fā)展的重要動力。在我國經(jīng)濟(jì)發(fā)展進(jìn)程中，各個中心城市向來是該地區(qū)經(jīng)濟(jì)和社會發(fā)展的“引路者”。于是，分析評價全國35各中心城市的綜合發(fā)展水平，無論是對城市自身的發(fā)展，還是對周邊地區(qū)的進(jìn)步，都具有十分重要的意義。下表是城市綜合發(fā)展水平的12項指標(biāo),試對全國35各中心城市的綜合發(fā)展水平做分析評價。xlx2x3x4x5x6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合月巴