由于模型是以特定時期的樣本所開發的，此模型是否適用于開發樣本之外的族群，必須經過穩定性測試才能得知。穩定度指標(population stability index ,PSI)可衡量測試樣本及模型開發樣本評分的的分布差異，為最常見的模型穩定度評估指針。其實PSI表示的就是按分數分檔后，針對不同樣本，或者不同時間的樣本，population分布是否有變化，就是看各個分數區間內人數占總人數的占比是否有顯著變化。公式如下：

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PSI實際應用范例：

1）樣本外測試

　　針對不同的樣本測試一下模型穩定度，比如訓練集與測試集，也能看出模型的訓練情況，我理解是看出模型的方差情況。

2）時間外測試

　　測試基準日與建模基準日相隔越遠，測試樣本的風險特征和建模樣本的差異可能就越大，因此PSI值通常較高。至此也可以看出模型建的時間太長了，是不是需要重新用新樣本建模了。

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Population Stability Index (PSI) – Our Banking Case Continues

The following is a representation for the latest quarterly comparison your team has performed against the benchmark sample. Here Actual %’ is the population distribution for the latest quarter and ‘Expected %’ is the population distribution for the validation sample (a.k.a. benchmark sample).

Comparing two populations visually is a good place to start. The current population seems to have shifted towards the right side of the graph. To a small extent, this is expected since scorecards often influence the through-the-door population as the market starts reacting to the approval strategies of the bank. However, the question we need to ask is whether this a major shift in the population? Essentially, you are comparing two different distributions and could use any goodness-of-fit measure such as Chi-square test. However, the population stability index is an industry-accepted metric that presents some convenient rules of thumb for the same. The population stability index (PSI) formula is displayed below (refer to ‘Credit Risk Scorecards’ by Naeem Siddiqui)

Again like the weight of evidence and the information value, PSI seems to have it’s root in information theory. Let’s calculate the population stability index (PSI) for our population (we have already seen a histogram for this above).

Score bands	Actual %	Expected %	Ac-Ex	ln(Ac/Ex)	Index
< 251	5%	8%	-3%	-0.47	0.014
251–290	6%	9%	-3%	-0.41	0.012
291–320	6%	10%	-4%	-0.51	0.020
321–350	8%	13%	-5%	-0.49	0.024
351–380	10%	12%	-2%	-0.18	0.004
381–410	12%	11%	1%	0.09	0.001
411–440	14%	10%	4%	0.34	0.013
441–470	14%	9%	5%	0.44	0.022
471–520	13%	9%	4%	0.37	0.015
520 <	9%	8%	1%	0.12	0.001
??Population Stability Index (PSI)=					0.1269

The last column in the above table is what we care for. Let us consider the score band 251-290 and calculate the index value for this row.

The final value for the PSI i.e. 0.13 is the sum of all the values of the last column. Now the question is how to interpret this value? The rule of thumb for the PSI is displayed below

PSI Value	Inference	Action
Less than 0.1	Insignificant change	No action required
0.1 – 0.25	Some minor change	Check other scorecard monitoring metrics
Greater than 0.25	Major shift in population	Need to delve deeper

The value of 0.13 falls in the second bucket which indicates a minor shift in population from the validation or benchmark sample. These are handy rules to have. However, one must ask, how is this population shift going to make any difference in the scorecard? Actually, it may or may not make any difference. Each score band of a scorecard has an associated bad rate or probability of customers not paying off their loans.? For instance, score band 251-290 in our scorecard has a bad rate of 10% or one customer out of the population of 10 in this score band won’t service his/her loan. The population stability index simply indicates changes in the population of loan applicants. However, this may or may not result in deterioration in performance of the scorecard to predict risk. Nevertheless, the PSI indicates changes in the environment which need to be further investigated through analyzing the change in macroeconomic conditions and overall lending policies of the bank.

參考https://www.cnblogs.com/webRobot/p/9133507.html?

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