--- GA: UA-159972578-2 --- ###### tags: `R` `TraMineR` `Sequential Pattern Mining` `Data Mining` `資料探勘` # TraMineR套件介紹 Reference: [Michael Hahsler(2011). "recommenderlab: A Framework for Developing and Testing Recommendation Algorithms."](http://traminer.unige.ch/) + 一個用於探索時序資料的套件 + 將隨著時間而變的狀態用視覺化方式呈現 + 使用場合: + 行銷漏斗轉換分析 + 社經事件追蹤研究 + 購物流程/行為分析 + 顧客價值分析(新顧客、忠誠顧客、沈睡顧客的轉變) + 常用function: + seqdef():create sequence obj. + seqdist():compute distance + seqient():compute entropy + seqtab():frequency table + seqistatd():individual sequence stat. + 畫圖function: + seqfplot():sequence frequency plots + seqmtplot():mean times plots(bar chart) + seqdplot():state distribution plots + seqHtplot():transversal entropy plots ## 變數表 對人做6年的職涯發展追蹤(1993七月~1999六月) | 變數 | 說明 | 舉例 | | -------- | -------- | -------- | | id | 獨一識別 | | weight | 隨機設定權重 | 0.13 ~ 4.46 (平均: 0.69) | | male | 性別 | 1 = 男, 0 = 女 | | catholic | 信仰 | 1 = 天主教, 0 = 新教 | | Belfast | 學校所在地 | Binary dummy | | N.Eastern | 學校所在地 | Binary dummy | | Southern | 學校所在地 | Binary dummy | | S.Eastern | 學校所在地 | Binary dummy | | Western | 學校所在地 | Binary dummy | | Grammar | 中等教育類型 | 1 = 語法學校 | | funemp | 父親的就業狀態 | 1 = Unemployed | | gcse5eq | 在義務教育結束時獲得的認證 | 1 = 5+GCSE分數為A-C,或同等 | | fmpr | 父親目前/最近的工作 | 1 = SOC1(專業/管理職相關) | | livboth | 首次調查時間(June 1995)的同居型態 | 1 = 與父母同住 | | jul93 | 每月活動狀態 | 1 = school, 2 = FE, 3 = employment, 4 = training, 5 = joblessness, 6=HE | | ... | ... | ... | | jun99 | 每月活動狀態 | 同上 | + FE(Further Education):any education after secondary school that is **not** an undergraduate or postgraduate degree. + HE(Higher Education):education at university. They come under two categories: **undergraduate** and **postgraduate**. ## 創建狀態序列 + seqdef(data):製作屬性如 alphabet, color palette and state labels 的狀態序列。以下說明之後會用到的optional參數: + alphabet:所有可能的狀態(自訂),內容至少要包含data中有出現的狀態。 + val:可以指定序列的欄位。 + states:必須與alphabet等長,顯示的文字。 + labels:顯示在Legend裡面的標籤。 ```{r} library(TraMineR) library(cluster) # load data data("mvad") # define attributes for state sequence object mvad.alphab = c("employment", "FE", "HE", "joblessness", "school", "training") # define state-seq object mvad.seq = seqdef(mvad, 17:86, xtstep = 6, alphabet = mvad.alphab) # 間距為六個月一格 ``` ``` 712 sequences in the data set min/max sequence length: 70/70 ``` ![](https://i.imgur.com/gTu4uyO.png) + 其他序列組合的表達方式 ```{r} print(mvad.seq[1:5, ], format = "SPS") ``` ``` Sequence [1] (EM,4)-(TR,2)-(EM,64) [2] (FE,36)-(HE,34) [3] (TR,24)-(FE,34)-(EM,10)-(JL,2) [4] (TR,47)-(EM,14)-(JL,9) [5] (FE,25)-(HE,45) ``` ## Individual Sequence Characteristics + seqistatd():序列中的對象的每個序列的狀態頻率(總持續時間)。 ```{r} seqistatd(mvad.seq[1:4, ]) ``` ``` [>] computing state distribution for 5 sequences ... employment FE HE joblessness school training 1 68 0 0 0 0 2 2 0 36 34 0 0 0 3 10 34 0 2 0 24 4 14 0 0 9 0 47 5 0 25 45 0 0 0 ``` ## 分群下的Sequential Pattern + 分群的基礎即是「距離」。 + seqdist(seqdata, method):Sequence Data計算距離的方法。 + Hamming distance (HAM):兩個字符串對應位置的不同字符的個數。 + ![](https://i.imgur.com/I4hvrNI.png =50%x) + ![](https://i.imgur.com/ZyJj8Ui.png =77%x) + Optimal Matching (OM) Edit Distance:最小Edit(插入/刪除)次數。(popular in social sciences) + ![](https://i.imgur.com/TAenNjw.png =60%x) + ![](https://i.imgur.com/Fhe5aFI.png =86%x) + Longest Common Prefix (LCP):counting the number of successive common positions starting from the beginning of the sequences. + Longest Common Suffix (RLCP):looks for the common elements from the end rather than from the beginning of the sequences. + Longest Common Subsequence (LCS) + Dynamic Hamming Distance (DHD) (Lesnard,2010) ![](https://i.imgur.com/2zFLqPS.png) ### 階層式分群(Hierarchical Clustering)方法:[詳細參考](https://www.jamleecute.com/hierarchical-clustering-%E9%9A%8E%E5%B1%A4%E5%BC%8F%E5%88%86%E7%BE%A4/) + 聚合法(AGNES, Agglomerative Nesting):由樹狀結構的底部開始開始逐次合併 (bottom-up),適合小規模。 + hclust() + agnes() + 能另外計算聚合係數(agglomerative coefficient)。 + 聚合係數是衡量群聚結構被辨識的程度,聚合係數越接近1代表有堅固的群聚結構(strong clustering structure)。 + 分裂法(DIANA, Divisive Analysis):由樹狀結構的頂部開始逐次分裂(top-down),適合大規模。 + diana() ```{r} # distance matrix mvad.om = seqdist(mvad.seq, method = "OM", indel = 1, sm = "TRATE") # clustering clusterward = agnes(mvad.om, diss = TRUE, method = "ward") # diss為True代表使用距離矩陣; Flase為觀察值矩陣 # 此使用華爾法 plot(clusterward) mvad.cl4 = cutree(clusterward, k = 4) # 分4群 cl4.lab = factor(mvad.cl4, labels = paste("Cluster", 1:4)) # 製作Label # sequence plot by clusters seqdplot(mvad.seq, group = cl4.lab, border = NA) ``` ![](https://i.imgur.com/0Og1Ipc.png) ![](https://i.imgur.com/BCNCLvW.png) + 第一個集群基本上是由年輕人組成,在結束義務教育後不久就成為勞動力。 + 接受教育的人在第二(高等教育)和第三集群中。 + 最後一個集群組不太成功,他們度過了長時間的失業或培訓工作。 ## Entropy + 此詞源自於熱力學,被用於計算一個系統中的失序現象(混亂的程度),介於0~1。 + 亂度愈大,Entropy愈趨近於1。 + 每個人的sequence pattern都不一樣,有的人很集中(entropy小),有的人很分散(entropy大)。例如:第一筆資料,4個月都在就業中,經過兩年的訓練後,64個月都在就業。 + seqient():Computes normalized or non-normalized within sequence entropies. ```{r} # regress to entropy (diversity) entropies = seqient(mvad.seq) # logitudinal entropy lm.ent = lm(entropies ~ male + funemp + gcse5eq, mvad) summary(lm.ent) ``` ``` Call: lm(formula = entropies ~ male + funemp + gcse5eq, data = mvad) Residuals: Min 1Q Median 3Q Max -0.45875 -0.09500 -0.00312 0.12795 0.46401 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.39078 0.01194 32.734 < 2e-16 *** maleyes -0.04024 0.01328 -3.031 0.00253 ** funempyes 0.02959 0.01774 1.668 0.09578 . gcse5eqyes 0.06797 0.01388 4.896 1.21e-06 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.1739 on 708 degrees of freedom Multiple R-squared: 0.05502, Adjusted R-squared: 0.05102 F-statistic: 13.74 on 3 and 708 DF, p-value: 1.017e-08 ``` + 在義務教育結束時獲得的認證(gcse5eqyes)顯著影響entropy ### Transversal entropy of state distributions ```{r} seqstatd(mvad.seq) seqHtplot(mvad.seq, group = mvad$gcse5eq) ``` ``` [State frequencies] Sep.93 Oct.93 Nov.93 Dec.93 Jan.94 Feb.94 Mar.94 Apr.94 May.94 Jun.94 Jul.94 Aug.94 employment 0.117 0.124 0.13 0.138 0.140 0.140 0.149 0.157 0.164 0.183 0.250 0.258 FE 0.386 0.388 0.38 0.381 0.369 0.364 0.361 0.353 0.347 0.326 0.275 0.275 HE 0.000 0.000 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 joblessness 0.024 0.021 0.02 0.021 0.028 0.038 0.034 0.035 0.039 0.048 0.079 0.069 school 0.251 0.246 0.24 0.242 0.240 0.242 0.240 0.240 0.239 0.232 0.197 0.195 training 0.222 0.222 0.22 0.219 0.222 0.216 0.216 0.215 0.211 0.212 0.199 0.202 Sep.94 Oct.94 Nov.94 Dec.94 Jan.95 Feb.95 Mar.95 Apr.95 May.95 Jun.95 Jul.95 Aug.95 employment 0.235 0.242 0.247 0.254 0.256 0.260 0.267 0.279 0.288 0.30 0.3778 0.3834 FE 0.310 0.312 0.309 0.308 0.306 0.296 0.295 0.285 0.281 0.27 0.1966 0.1938 HE 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00 0.0042 0.0042 joblessness 0.049 0.052 0.049 0.051 0.056 0.065 0.063 0.067 0.066 0.08 0.0815 0.0857 school 0.201 0.202 0.202 0.201 0.202 0.201 0.201 0.199 0.199 0.20 0.2093 0.2093 training 0.205 0.192 0.192 0.187 0.180 0.178 0.174 0.169 0.166 0.16 0.1306 0.1236 Sep.95 Oct.95 Nov.95 Dec.95 Jan.96 Feb.96 Mar.96 Apr.96 May.96 Jun.96 Jul.96 Aug.96 employment 0.428 0.413 0.416 0.416 0.423 0.421 0.433 0.440 0.442 0.455 0.545 0.551 FE 0.213 0.192 0.191 0.190 0.185 0.185 0.176 0.176 0.174 0.171 0.117 0.117 HE 0.073 0.159 0.163 0.163 0.160 0.159 0.159 0.159 0.159 0.157 0.150 0.149 joblessness 0.086 0.080 0.079 0.079 0.080 0.084 0.086 0.079 0.077 0.074 0.081 0.083 school 0.081 0.042 0.041 0.041 0.038 0.038 0.038 0.038 0.038 0.038 0.025 0.024 training 0.118 0.114 0.111 0.112 0.114 0.112 0.110 0.110 0.110 0.104 0.081 0.077 Sep.96 Oct.96 Nov.96 Dec.96 Jan.97 Feb.97 Mar.97 Apr.97 May.97 Jun.97 Jul.97 Aug.97 employment 0.544 0.532 0.531 0.534 0.537 0.541 0.542 0.551 0.553 0.562 0.603 0.605 FE 0.115 0.111 0.112 0.112 0.111 0.111 0.107 0.105 0.104 0.101 0.062 0.062 HE 0.176 0.206 0.208 0.206 0.205 0.205 0.206 0.204 0.204 0.201 0.190 0.190 joblessness 0.083 0.079 0.079 0.079 0.083 0.083 0.086 0.084 0.086 0.084 0.110 0.112 school 0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 training 0.072 0.072 0.070 0.069 0.065 0.060 0.059 0.056 0.053 0.052 0.037 0.031 Sep.97 Oct.97 Nov.97 Dec.97 Jan.98 Feb.98 Mar.98 Apr.98 May.98 Jun.98 Jul.98 Aug.98 employment 0.611 0.610 0.619 0.622 0.622 0.624 0.628 0.631 0.632 0.638 0.670 0.677 FE 0.052 0.041 0.041 0.041 0.038 0.037 0.037 0.037 0.035 0.035 0.020 0.020 HE 0.198 0.215 0.215 0.213 0.212 0.212 0.211 0.209 0.209 0.206 0.181 0.176 joblessness 0.105 0.103 0.094 0.093 0.098 0.104 0.101 0.100 0.101 0.100 0.114 0.112 school 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 training 0.034 0.032 0.031 0.031 0.029 0.024 0.024 0.024 0.022 0.021 0.015 0.015 Sep.98 Oct.98 Nov.98 Dec.98 Jan.99 Feb.99 Mar.99 Apr.99 May.99 Jun.99 employment 0.673 0.677 0.680 0.676 0.680 0.681 0.678 0.678 0.677 0.680 FE 0.020 0.013 0.011 0.011 0.013 0.013 0.013 0.013 0.013 0.013 HE 0.170 0.177 0.176 0.176 0.174 0.173 0.173 0.171 0.169 0.166 joblessness 0.119 0.115 0.117 0.119 0.115 0.119 0.124 0.125 0.131 0.131 school 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 training 0.018 0.018 0.017 0.018 0.018 0.014 0.013 0.013 0.011 0.011 [Valid states] Sep.93 Oct.93 Nov.93 Dec.93 Jan.94 Feb.94 Mar.94 Apr.94 May.94 Jun.94 Jul.94 Aug.94 N 712 712 712 712 712 712 712 712 712 712 712 712 Sep.94 Oct.94 Nov.94 Dec.94 Jan.95 Feb.95 Mar.95 Apr.95 May.95 Jun.95 Jul.95 Aug.95 N 712 712 712 712 712 712 712 712 712 712 712 712 Sep.95 Oct.95 Nov.95 Dec.95 Jan.96 Feb.96 Mar.96 Apr.96 May.96 Jun.96 Jul.96 Aug.96 N 712 712 712 712 712 712 712 712 712 712 712 712 Sep.96 Oct.96 Nov.96 Dec.96 Jan.97 Feb.97 Mar.97 Apr.97 May.97 Jun.97 Jul.97 Aug.97 N 712 712 712 712 712 712 712 712 712 712 712 712 Sep.97 Oct.97 Nov.97 Dec.97 Jan.98 Feb.98 Mar.98 Apr.98 May.98 Jun.98 Jul.98 Aug.98 N 712 712 712 712 712 712 712 712 712 712 712 712 Sep.98 Oct.98 Nov.98 Dec.98 Jan.99 Feb.99 Mar.99 Apr.99 May.99 Jun.99 N 712 712 712 712 712 712 712 712 712 712 [Entropy index] Sep.93 Oct.93 Nov.93 Dec.93 Jan.94 Feb.94 Mar.94 Apr.94 May.94 Jun.94 Jul.94 Aug.94 H 0.77 0.77 0.78 0.78 0.79 0.8 0.8 0.81 0.82 0.83 0.86 0.85 Sep.94 Oct.94 Nov.94 Dec.94 Jan.95 Feb.95 Mar.95 Apr.95 May.95 Jun.95 Jul.95 Aug.95 H 0.84 0.84 0.84 0.84 0.84 0.85 0.84 0.85 0.84 0.85 0.84 0.84 Sep.95 Oct.95 Nov.95 Dec.95 Jan.96 Feb.96 Mar.96 Apr.96 May.96 Jun.96 Jul.96 Aug.96 H 0.87 0.87 0.87 0.87 0.86 0.86 0.86 0.85 0.85 0.84 0.76 0.76 Sep.96 Oct.96 Nov.96 Dec.96 Jan.97 Feb.97 Mar.97 Apr.97 May.97 Jun.97 Jul.97 Aug.97 H 0.74 0.72 0.72 0.72 0.72 0.71 0.71 0.7 0.7 0.69 0.65 0.64 Sep.97 Oct.97 Nov.97 Dec.97 Jan.98 Feb.98 Mar.98 Apr.98 May.98 Jun.98 Jul.98 Aug.98 H 0.63 0.62 0.61 0.6 0.6 0.6 0.59 0.59 0.59 0.58 0.54 0.53 Sep.98 Oct.98 Nov.98 Dec.98 Jan.99 Feb.99 Mar.99 Apr.99 May.99 Jun.99 H 0.54 0.53 0.52 0.53 0.53 0.52 0.52 0.52 0.52 0.52 ``` ![](https://i.imgur.com/0sqrXXP.png) + Entropy都很高,代表亂度大(隨機分佈) + 在義務教育結束時獲得的認證(1=yes=5+GCSE分數為A-C,或同等)較多的,其Entropy指數變化劇烈(有波鋒) ## Sequence Frquency + seqtab():計算序列的頻率及比例表。 ```{r} mvad.lab <- c("Employment", "Further education", "Higher education", "Joblessness", "School", "Training") mvad.scode <- c("EM", "FE", "HE", "JL", "SC", "TR") mvad.seq <- seqdef(mvad, 17:86, alphabet = mvad.alphab, states = mvad.scode, labels = mvad.lab, xtstep = 6) seqtab(mvad.seq, tlim = 1:10) ``` ``` Freq Percent EM/70 50 7.02 TR/22-EM/48 18 2.53 FE/22-EM/48 17 2.39 SC/24-HE/46 16 2.25 SC/25-HE/45 13 1.83 FE/25-HE/45 8 1.12 FE/34-EM/36 7 0.98 FE/46-EM/24 7 0.98 FE/10-EM/60 6 0.84 FE/24-HE/46 6 0.84 ``` ### Weighted Sequence(加入權重) ```{r} mvad.seq <- seqdef( mvad, 17:86, alphabet = mvad.alphab, states = mvad.scode, labels = mvad.lab, weights = mvad$weight, xtstep = 6) seqtab(mvad.seq, tlim = 1:10) ``` ``` Freq Percent SC/24-HE/46 33.4 4.70 SC/25-HE/45 24.6 3.46 TR/22-EM/48 17.9 2.51 EM/70 15.2 2.13 FE/22-EM/48 11.0 1.54 SC/24-EM/46 10.9 1.53 SC/37-HE/33 9.8 1.38 SC/34-EM/36 7.0 0.98 FE/25-HE/45 6.7 0.95 TR/21-EM/49 5.9 0.82 ``` ### Weighted & Unweighted 比較 ```{r} par(mfrow = c(2, 1)) seqfplot(mvad.seq, border = NA, withlegend = FALSE, title = "Weighted frequencies") seqfplot(mvad.seq, weighted = FALSE, border = NA, withlegend = FALSE, title = "Unweighted frequencies") ``` ![](https://i.imgur.com/0DGUEYG.png) + 抓出前10大Percent的序列 + 根據自訂Weight的不同,會對pattern的結果有很大的影響(抑制/增幅)。 ## 特徵變數下的Squence統計 ```{r} seqmtplot(mvad.seq, group = mvad$funemp, ylim = c(0, 30)) ``` ![](https://i.imgur.com/7vMQJEw.png) + 父親的就業狀態(1=yes=Unemployed)為失業的話: + 子女在高等教育(HE)的平均時長較短 + 子女沒工作(joblessness)的平均時長較長 + 子女在校(school)的平均時長較短 + 子女接受訓練(training)的平均時長較長 ```{r} by(mvad.seq, mvad$funemp, seqmeant) ``` ``` mvad$funemp: no Mean employment 31.8 FE 11.7 HE 9.2 joblessness 4.6 school 6.0 training 6.6 --------------------------------------------------------------------------- mvad$funemp: yes Mean employment 31.2 FE 10.0 HE 4.3 joblessness 10.9 school 4.1 training 9.5 ``` ## 狀態轉移矩陣 + seqtrate():計算狀態之間的transition rate。 ```{r} seqtrate(mvad.seq) %>% round(2) ``` ``` [-> employment] [-> FE] [-> HE] [-> joblessness] [-> school] [-> training] [employment ->] 0.99 0.00 0.00 0.01 0.00 0.00 [FE ->] 0.03 0.95 0.01 0.01 0.00 0.00 [HE ->] 0.01 0.00 0.99 0.00 0.00 0.00 [joblessness ->] 0.04 0.01 0.00 0.94 0.00 0.01 [school ->] 0.01 0.01 0.02 0.01 0.95 0.00 [training ->] 0.04 0.00 0.00 0.01 0.00 0.94 ``` + 就業(employment)接續維持原狀態的機率為0.99,而有0.01的機率可能會失業(joblessness)。 + 高中教育(FE)接續維持原狀態的機率為0.95,有0.03可能轉移至就業,0.01的機率則會晉升到大學教育(HE)或退回失業狀態。 + 根據馬可夫原理,經過長時間的改變後,轉移矩陣在每個狀態下的人數會趨近於一個穩定平衡的狀態。 ### 馬可夫鏈(Markov Chain) + 從一個狀態到另一個狀態的轉換的隨機過程,並且移動到每一個點的機率都是相同的。 + 該過程要求具備「無記憶」的性質:下一狀態的機率分布只能由當下狀態決定,與時間序列前面的事件無關。 + 使用情境: + 在一個Mechanical的系統下(變動不會太大) + 在推出新產品時,去估計自己產品推出後與市場上的競爭,在長期下的市佔率 ![](https://i.imgur.com/gWy484N.png =50%x) + 平衡狀態下,流進人數=流出人數: 0.3E+0.4E=0.7A 0.7E+0.6A=0.4E ## 轉移狀態的分佈 ```{r} seqstatd(mvad.seq[, 1:8]) ``` ``` [State frequencies] Sep.93 Oct.93 Nov.93 Dec.93 Jan.94 Feb.94 Mar.94 Apr.94 employment 0.117 0.124 0.13 0.138 0.140 0.140 0.149 0.157 FE 0.386 0.388 0.38 0.381 0.369 0.364 0.361 0.353 HE 0.000 0.000 0.00 0.000 0.000 0.000 0.000 0.000 joblessness 0.024 0.021 0.02 0.021 0.028 0.038 0.034 0.035 school 0.251 0.246 0.24 0.242 0.240 0.242 0.240 0.240 training 0.222 0.222 0.22 0.219 0.222 0.216 0.216 0.215 [Valid states] Sep.93 Oct.93 Nov.93 Dec.93 Jan.94 Feb.94 Mar.94 Apr.94 N 712 712 712 712 712 712 712 712 [Entropy index] Sep.93 Oct.93 Nov.93 Dec.93 Jan.94 Feb.94 Mar.94 Apr.94 H 0.77 0.77 0.78 0.78 0.79 0.8 0.8 0.81 ``` ### 狀態分佈圖 by 特徵變數 ```{r} seqdplot(mvad.seq, group = mvad$gcse5eq, border = NA) ``` ![](https://i.imgur.com/WkuDms4.png) ### Sequence of modal states + Modal State:最大(多)的狀態序列 ```{r} seqmodst(mvad.seq) seqmsplot(mvad.seq, group = mvad$gcse5eq, border = NA) ``` ``` [Modal state sequence] Sequence 1 FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-FE-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment-employment [State frequencies] Sep.93 Oct.93 Nov.93 Dec.93 Jan.94 Feb.94 Mar.94 Apr.94 May.94 Jun.94 Jul.94 Aug.94 Sep.94 Freq. 0.39 0.39 0.38 0.38 0.37 0.36 0.36 0.35 0.35 0.33 0.28 0.28 0.31 Oct.94 Nov.94 Dec.94 Jan.95 Feb.95 Mar.95 Apr.95 May.95 Jun.95 Jul.95 Aug.95 Sep.95 Oct.95 Freq. 0.31 0.31 0.31 0.31 0.3 0.29 0.29 0.29 0.3 0.38 0.38 0.43 0.41 Nov.95 Dec.95 Jan.96 Feb.96 Mar.96 Apr.96 May.96 Jun.96 Jul.96 Aug.96 Sep.96 Oct.96 Nov.96 Freq. 0.42 0.42 0.42 0.42 0.43 0.44 0.44 0.46 0.54 0.55 0.54 0.53 0.53 Dec.96 Jan.97 Feb.97 Mar.97 Apr.97 May.97 Jun.97 Jul.97 Aug.97 Sep.97 Oct.97 Nov.97 Dec.97 Freq. 0.53 0.54 0.54 0.54 0.55 0.55 0.56 0.6 0.61 0.61 0.61 0.62 0.62 Jan.98 Feb.98 Mar.98 Apr.98 May.98 Jun.98 Jul.98 Aug.98 Sep.98 Oct.98 Nov.98 Dec.98 Jan.99 Freq. 0.62 0.62 0.63 0.63 0.63 0.64 0.67 0.68 0.67 0.68 0.68 0.68 0.68 Feb.99 Mar.99 Apr.99 May.99 Jun.99 Freq. 0.68 0.68 0.68 0.68 0.68 ``` ![](https://i.imgur.com/j9481tc.png) + 結合上圖來看,No群的人在1993年九月最多人是處於高中教育(FE),在1994九月以後皆為就業狀態。