第五章 結論與討論
第五節 綜合討論
除了參數本身的估計值及估計標準誤之外，從取樣次數及其估計分配探討對 於結果的影響。根據中央極限定理，從平均數μ 標準差σ 的母群體中，重複抽取n 個觀察值為一組樣本，若樣本數n愈大，則樣本平均數（Xn ）分配愈趨近常態分 配（Hogg & Tanis, 2005; Freund & Wilson, 2003），因此取樣數愈多則標準差愈小。
另外根據大數法則(Law of Large Number)，當取樣數n趨近於無窮大時，樣本平均 數Xn 與母體平均數μ 之差落在一個小範圍（ε）的機率趨近於1，因此取樣數愈 多，參數估計的愈精確。然而上述兩定理都僅針對於取樣數需趨近於無窮大，而 對於取樣次數M究竟需要多少才算足夠並無定論，且相關文獻中亦無明確次數可 遵循，因而Asparouhov(2005, 2006)、Stapleton(2002, 2006, 2008)、Blume與Royall (2003)、Pfeffermann等人（1998）及Yang與Tsai(2006)等相關研究分別以200至1000 等不同取樣次數（重複實驗次數），探討取樣權重對於迴歸模式、潛在變項模式、
階層線性模式、潛在類別模式、多層次模式等估計影響研究。而本研究選擇以500 做為取樣次數，不若Stapleton(2002, 2006, 2008)選擇1000次的取樣，但由於本研 究除了取樣次數之外並以四種重複取樣程序探討不同取樣設計及其取樣權重對 於CFA模式估算的影響，因此在相關的取樣及模式運算需要相當冗長的時間。據 此，選擇同Asparouhov(2005, 2006)的500次重複實驗。
從500次估計值的分配來看，不論是PPS或Str. RS取樣設計，四種重複取樣程
序的參數估計值分配都相當的近似，且取樣數愈多參數的估計值愈集中，其中以 取樣數240的參數估計分配最為分散，而PSU間的異質性愈大則參數估計的分配亦 愈分散。同理，參數估計值標準誤的分配亦是相同趨勢，但RG程序所呈現的趨 勢更是明顯且因標準誤的計算公式而導致其更接近於0。
綜合上述的結果及討論，若依據Stapleton(2002)及Hoogland與Boomsma(1998) 建議的參數估計及參數估計標準誤偏誤絕對值應分別小於5%及10%為標準，在面 對複雜資料結構或多階段取樣設計的資料時，研究者欲應用CFA模式進行資料分 析，本研究建議採用PPS取樣設計抽取資料並計算權重，至於重複取樣程序則選 擇JRR、Bootstrap或ABB都能達到較準確且穩定的參數估計及參數估計標準誤。
由於本研究是在有限的模擬設計情境，分別進行PPS及Str. RS設計下，其權 重計算及不同重複取樣程序對於CFA模式參數估算的影響，其推論也是在有限的 實驗條件下的結果，因此兩種取樣設計及其權重計算與重複取樣的程序在不同實 驗設計條件下對於參數估算的影響亦需更進一步進行相關研究。
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附錄
附錄一 連續資料下之參數估計及參數估計標準誤 偏誤與MSE
附表1-1 連續資料下之參數（λ2）估計偏誤
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 .0001 .0001 .0001 0001 .0001 -.0093 .0031 -.0017 1200 .0000 .0001 .0000 .0001 .0092 .0006 .0039 .0030 2400 .0000 .0001 .0000 .0001 -.0035 -.0029 .0035 -.0020 JRR
4800 .0000 .0000 .0000 .0000 .0009 -.0036 .0040 -.0036 240 .0020 .0012 .0033 .0005 .0009 -.0061 .0056 .0006 1200 .0007 .0009 .0007 .0005 .0095 .0009 .0037 .0036 2400 -.0006 .0008 .0003 .0000 -.0027 -.0028 .0039 -.0015 Bootstrap
4800 -.0006 .0003 .0002 -.0001 .0007 -.0034 .0039 -.0034 240 .0013 .0014 .0017 .0014 .0018 -.0067 .0059 .0004 1200 .0003 .0003 .0003 .0003 .0092 .0010 .0039 .0032 2400 .0001 .0002 .0002 .0002 -.0031 -.0026 .0036 -.0018 ABB
4800 .0001 .0001 .0002 .0001 .0008 -.0035 .0040 -.0033 240 .0047 .0184 .0056 .0159 .0156 .0082 .0134 .0115 1200 .0054 .0011 .0004 .0010 .0097 -.0005 .0035 .0062 2400 -.0005 -.0004 .0027 -.0003 -.0052 -.0032 .0041 .0004 RG
4800 .0009 .0039 .0019 .0000 .0031 -.0026 .0029 -.0035
附表1-2 連續資料下之參數（λ2）估計MSE
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 .0032 .0022 .0019 .0018 .0026 .0026 .0022 .0026 1200 .0014 .0009 .0005 .0005 .0008 .0007 .0006 .0005 2400 .0011 .0007 .0004 .0002 .0005 .0004 .0003 .0003 JRR
4800 .0011 .0006 .0004 .0001 .0003 .0002 .0002 .0001 240 .0032 .0022 .0020 .0018 .0026 .0026 .0022 .0026 1200 .0014 .0009 .0005 .0005 .0008 .0008 .0006 .0005 2400 .0011 .0007 .0004 .0002 .0005 .0004 .0003 .0003 Bootstrap
4800 .0010 .0006 .0004 .0001 .0003 .0003 .0002 .0001 240 .0031 .0023 .0020 .0018 .0026 .0026 .0022 .0026 1200 .0014 .0009 .0005 .0005 .0008 .0007 .0006 .0005 2400 .0010 .0007 .0004 .0002 .0005 .0004 .0003 .0003 ABB
4800 .0010 .0006 .0004 .0001 .0003 .0003 .0002 .0001 240 .0032 .0022 .0017 .0027 .0029 .0022 .0022 .0023 1200 .0015 .0013 .0006 .0005 .0009 .0007 .0005 .0007 2400 .0012 .0006 .0005 .0002 .0008 .0004 .0004 .0003 RG
4800 .0007 .0007 .0003 .0001 .0003 .0002 .0001 .0001
附表1-3 連續資料下參數估計（λ2）標準誤偏誤
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 -.0366 .0336 .0377 -.0201 -.1574 -.0117 .0664 .0899 1200 .0333 .0445 .0800 -.0746 -.4055 -.3022 -.2019 .0387 2400 .0950 .0299 .0167 .0695 -.4381 -.4157 -.1897 .0413 JRR
4800 -.0238 .0631 -.0320 -.0248 -.4417 -.4266 -.3977 -.0961 240 -.0306 .0364 .0428 -.0143 -.1384 -.0016 .0870 .1079 1200 .0223 .0353 .0964 -.0660 -.3859 -.2892 -.1911 .0370 2400 .0875 .0189 .0154 .0545 -.4068 -.3962 -.1870 .0324 Bootstrap
4800 -.0247 .0611 -.0503 -.0368 -.3998 -.3577 -.3702 -.0947 240 -.0358 .0468 .0426 -.0224 -.1258 .0017 .0935 .1284 1200 .0322 .0399 .0820 -.0672 -.3778 -.2918 -.1903 .0375 2400 .0888 .0304 .0137 .0768 -.4137 -.3934 -.1819 .0368 ABB
4800 -.0202 .0622 -.0379 -.0222 -.4010 -.3632 -.3784 -.0823 240 -.1937 -.0648 -.0731 -.0640 -.1667 -.0223 .0719 .1414 1200 -.4974 -.3762 -.2611 -.2451 -.5634 -.4577 -.3049 -.0098 2400 -.5833 -.5098 -.3882 -.2468 -.6636 -.5782 -.3443 -.0652 RG
4800 -.7300 -.6308 -.5544 -.3092 -.7426 -.6428 -.5571 -.2269
附表1-4 連續資料下參數（λ2）估計標準誤MSE
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 .0019 .0013 .0011 .0011 .0029 .0018 .0012 .0010 1200 .0008 .0005 .0003 .0003 .0020 .0010 .0006 .0003 2400 .0006 .0004 .0002 .0001 .0015 .0010 .0004 .0002 JRR
4800 .0006 .0003 .0002 .0001 .0015 .0008 .0004 .0001 240 .0001 .0001 .0001 .0001 .0005 .0002 .0002 .0002 1200 .0001 .0000 .0000 .0000 .0005 .0002 .0001 .0000 2400 .0001 .0000 .0000 .0000 .0003 .0002 .0000 .0000 Bootstrap
4800 .0000 .0000 .0000 .0000 .0003 .0002 .0001 .0000 240 .0001 .0001 .0001 .0001 .0005 .0002 .0002 .0002 1200 .0001 .0000 .0000 .0000 .0005 .0002 .0001 .0000 2400 .0001 .0000 .0000 .0000 .0003 .0002 .0000 .0000 ABB
4800 .0000 .0000 .0000 .0000 .0004 .0002 .0001 .0000 240 .0022 .0015 .0010 .0020 .0017 .0014 .0013 .0013 1200 .0010 .0009 .0004 .0003 .0006 .0005 .0003 .0005 2400 .0007 .0004 .0003 .0001 .0006 .0002 .0003 .0002 RG
4800 .0004 .0004 .0002 .0001 .0002 .0001 .0001 .0001
附錄二 類別資料下之參數估計及參數估計標準誤 偏誤與MSE表現
附表2-1 類別資料下之參數（λ2）估計偏誤
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 .0001 .0001 .0001 .0000 .0026 .0069 -.0001 -.0130 1200 .0000 .0000 .0000 .0000 .0061 .0097 .0064 -.0118 2400 .0000 .0000 .0000 .0000 .0075 .0067 .0031 -.0118 JRR
4800 .0000 .0000 .0000 .0000 .0047 .0009 .0006 -.0130 240 -.0020 -.0001 .0000 .0004 .0013 .0093 -.0008 -.0132 1200 -.0003 .0002 -.0003 .0001 .0066 .0096 .0069 -.0112 2400 -.0003 -.0002 -.0002 .0003 .0069 .0065 .0029 -.0121 Bootstrap
4800 -.0001 .0000 .0005 -.0001 .0041 .0009 .0005 -.0126 240 .0003 .0006 .0008 .0010 .0026 .0086 .0009 -.0113 1200 .0000 -.0002 -.0001 .0001 .0058 .0093 .0061 -.0116 2400 -.0001 .0000 .0000 -.0001 .0071 .0063 .0029 -.0116 ABB
4800 -.0002 -.0001 -.0001 .0000 .0047 .0005 .0006 -.0127 240 .0006 .0016 -.0046 -.0027 .0055 .0185 -.0007 -.0209 1200 .0015 .0007 .0030 -.0001 .0022 .0079 .0043 -.0122 2400 -.0043 .0004 -.0044 .0013 .0104 .0050 .0061 -.0155 RG
4800 -.0006 .0020 .0020 .0004 .0047 .0022 -.0005 -.0136
附表2-2 類別資料下之參數（λ2）估計MSE
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 .0059 .0037 .0032 .0034 .0048 .0042 .0044 .0039 1200 .0014 .0009 .0008 .0006 .0010 .0010 .0009 .0008 2400 .0011 .0008 .0005 .0003 .0007 .0004 .0005 .0004 JRR
4800 .0008 .0005 .0004 .0002 .0003 .0003 .0002 .0002 240 .0038 .0037 .0033 .0034 .0047 .0042 .0044 .0038 1200 .0014 .0009 .0008 .0006 .0010 .0011 .0008 .0008 2400 .0011 .0008 .0005 .0003 .0007 .0004 .0005 .0004 Bootstrap
4800 .0008 .0005 .0004 .0002 .0003 .0004 .0002 .0002 240 .0038 .0037 .0032 .0034 .0047 .0042 .0044 .0039 1200 .0014 .0009 .0008 .0006 .0010 .0010 .0008 .0008 2400 .0011 .0008 .0005 .0003 .0007 .0004 .0005 .0004 ABB
4800 .0008 .0005 .0004 .0002 .0003 .0004 .0002 .0002 240 .0048 .0049 .0057 .0027 .0034 .0050 .0030 .0040 1200 .0014 .0010 .0004 .0007 .0015 .0010 .0005 .0009 2400 .0007 .0008 .0005 .0003 .0003 .0004 .0004 .0005 RG
4800 .0008 .0004 .0003 .0002 .0003 .0004 .0002 .0003
附表2-3 類別資料下參數（λ2）估計標準誤偏誤
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 -.0315 -.0744 .0182 -.0954 .0394 .1042 .1103 .1241 1200 -.0507 -.0314 .0035 .0262 -.2270 -.1867 .0107 .1008 2400 -.0419 -.0675 .0428 .0358 -.3673 -.2577 -.1288 .1128 JRR
4800 .0395 .0937 -.0167 .0883 -.3925 -.4197 -.1919 .0031 240 -.0304 -.0682 .0172 -.1076 .0456 .1220 .1111 .1059 1200 -.0576 -.0336 .0029 .0296 -.2154 -.1802 -.0023 .0499 2400 -.0409 -.0697 .0629 .0375 -.3461 -.2484 -.1196 .0918 Bootstrap
4800 .0351 .0861 -.0240 .0816 -.3526 -.3952 -.1673 -.0113 240 -.0315 -.0716 .0246 -.1146 .0525 .1126 .1193 .1200 1200 -.0433 -.0256 -.0020 .0206 -.2059 -.1784 .0086 .0397 2400 -.0462 -.0685 .0407 .0386 -.3468 -.2400 -.1233 .0940 ABB
4800 .0383 .0906 -.0217 .0895 -.3619 -.3930 -.1790 .0048 240 -.1217 -.1088 .0171 -.0966 .0534 .1071 .1492 .2139 1200 -.3855 -.2669 -.1793 -.0798 -.3694 -.2770 -.0937 .1684 2400 -.5102 -.4219 -.2648 -.0663 -.5323 -.4081 -.2073 .0047 RG
4800 -.5883 -.4600 -.4073 -.0326 -.6312 -.5864 -.3408 -.1311
附表2-4 類別資料下參數（λ2）估計標準誤MSE
Difference of factor loading (d)
PPS Str. RS
n 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 240 .0020 .0022 .0019 .0021 .0024 .0022 .0019 .0012 1200 .0009 .0005 .0004 .0003 .0014 .0009 .0006 .0003 2400 .0006 .0005 .0003 .0002 .0012 .0007 .0004 .0002 JRR
4800 .0005 .0002 .0002 .0001 .0009 .0008 .0003 .0001 240 .0002 .0002 .0001 .0002 .0004 .0004 .0004 .0006 1200 .0000 .0000 .0000 .0000 .0002 .0001 .0001 .0001 2400 .0000 .0000 .0000 .0000 .0002 .0001 .0000 .0000 Bootstrap
4800 .0000 .0000 .0000 .0000 .0002 .0002 .0000 .0000 240 .0002 .0002 .0001 .0002 .0004 .0003 .0003 .0005 1200 .0000 .0000 .0000 .0000 .0002 .0001 .0001 .0001 2400 .0000 .0000 .0000 .0000 .0002 .0001 .0000 .0000 ABB
4800 .0000 .0000 .0000 .0000 .0002 .0002 .0000 .0000 240 .0035 .0030 .0042 .0016 .0020 .0033 .0020 .0027 1200 .0010 .0006 .0003 .0005 .0010 .0007 .0003 .0006 2400 .0003 .0005 .0003 .0002 .0002 .0002 .0003 .0003 RG
4800 .0005 .0002 .0002 .0001 .0002 .0002 .0001 .0002
附錄三 PPS在連續資料之參數（ λ
2）估計值分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖3-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖3-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖3-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖3-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計分配圖
附錄四 Str. RS在連續資料之參數（ λ
2）估計值分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖4-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖4-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖4-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖4-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計分配圖
附錄五 PPS在連續資料之參數（ λ
2）估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖5-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計標準誤分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖5-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計標準誤分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖5-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計標準誤分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖5-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計標準誤分配圖
附錄六 Str. RS在連續資料之參數 （ λ
2） 估計標準誤分 配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖6-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖6-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖6-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖6-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計標準誤分配
附錄七 PPS在類別資料之參數（ λ
2）估計值分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖7-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖7-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖7-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖7-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計分配圖
附錄八 Str. RS在類別資料之參數（ λ
2）估計值分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖8-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖8-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖8-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖8-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計分配圖
附錄九 PPS在類別資料之參數（ λ
2）估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖9-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計標準誤分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖9-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計標準誤分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖9-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計標準誤分配圖
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖9-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計標準誤分配圖
附錄十 Str. RS在類別資料之參數（ λ
2）估計標準誤 分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖10-1 因素負荷量差距 0.1 (d = 0.1) 之參數估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖10-2 因素負荷量差距 0.2 (d = 0.2) 之參數估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖10-3 因素負荷量差距 0.3 (d = 0.3) 之參數估計標準誤分配
JRR Bootstrap ABB RG
=10 n
=50 n
=100 n
=200 n
附圖10-4 因素負荷量差距 0.4 (d = 0.4) 之參數估計標準誤分配