Happiness is something we all aspire to, yet its key factors are still unclear.

幸福是我們所有人都渴望的東西，但其關鍵因素仍不清楚。

Some would argue that wealth is the most important condition as it determines one’s living conditions. Nevertheless, some would rightly point out that rich people aren’t systematically happy. On the contrary, one’s social relationships (family, friends, etc.) contribute just as much to his happiness. Finally, some would argue that the policies implemented by governments are what really determine one’s happiness, as they determine indirectly our living conditions and social interactions.

有人會說， 財富是最重要的條件，因為它決定著一個人的生活條件。 不過，有些人會正確地指出，有錢人并不系統地感到高興。 相反，一個人的社會關系 (家庭，朋友等)對他的幸福同樣重要。 最后，有人會說，政府實施的政策真正決定一個人的幸福，因為它們間接地決定了我們的生活條件和社會互動。

These are all general and intuitive ideas about happiness, that we can easily apprehend using our own experience. However, I believe that a data-driven approach would allow for a deeper understanding of happiness drivers. By applying the most advanced techniques of Machine Learning, it would be possible to define the most important factors and measure quantitatively their contribution to one’s happiness.

這些都是關于幸福的一般而直觀的想法，我們可以利用自己的經驗輕松地理解它們。 但是，我認為，數據驅動的方法可以使人們對幸福驅動力有更深的了解。 通過應用最先進的機器學習技術，可以定義最重要的因素，并定量地衡量它們對一個人的幸福的貢獻。

In this context, I analyzed data from The World Happiness Report which is a landmark survey of the state of global happiness. It contains, on the one hand, happiness scores based on the answers gathered from the Gallup World Poll (GWP) and on the other hand, indicators of economic production, social support, life expectancy, freedom, absence of corruption, and generosity.

在這種情況下，我分析了《世界幸福報告》中的數據， 該報告是全球幸福狀況的里程碑式調查。 它一方面包含基于蓋洛普世界民意測驗 (GWP)收集的答案的幸福分數，另一方面包含經濟生產，社會支持，預期壽命，自由，沒有腐敗和慷慨的指標。

This article is the second article of a series, where I share the key findings of the in-depth study I conducted on the subject. In my previous article, I analyzed happiness from a purely descriptive point of view. I discussed thus the complex relationships between happiness and three essential elements: wealth, social relations, and public policy. This data exploratory analysis lifted the veil on the difference that exists between the regions of the world over time.

本文是該系列文章的第二篇，在這里我分享了我對該主題進行的深入研究的主要發現。 在上一篇文章中 ，我從純粹描述性的角度分析了幸福。 因此，我討論了幸福與三個基本要素之間的復雜關系：財富，社會關系和公共政策。 這項數據探索性分析揭開了世界各地之間隨時間推移而存在的差異的面紗。

However, it is purely descriptive. It tells us nothing about the most crucial questions: what really brings happiness, to what extent, and why? This article intends to answer these questions by focusing on the causal relationship between happiness and the other variables, using statistical tools and Machine Learning.

但是，它純粹是描述性的。 它沒有告訴我們最關鍵的問題： 什么真正地帶來了幸福，程度如何，為什么？ 本文旨在通過使用統計工具和機器學習關注幸福感與其他變量之間的因果關系來回答這些問題。

In this perspective, I relied on two approaches: one ‘traditional’ approach commonly used in the field of economics and a new approach based on the state of the art Machine Learning interpretation tools.

從這個角度來看，我依靠兩種方法：一種是經濟學領域常用的“傳統”方法，另一種是基于最新的機器學習解釋工具的新方法。

Without more ado, let’s dive into the micro and macro-econometric of happiness!

事不宜遲，讓我們深入了解幸福的微觀和宏觀計量！

Structure:

結構體：

1. About the Data

   關于數據

2. ‘Classical’ Approach

   “古典”方法

3. Machine Learning Approach

   機器學習方法

4. Limitations

   局限性

1.關于數據 (1. About the Data)

Here a quick recap of the variables of the World Happiness Report dataset. For more information about the data, you can refer to my previous article here.

這里是世界幸福報告數據集變量的快速回顧。 有關數據的更多信息，您可以在此處參考我的上一篇文章。

Economic metrics:

經濟指標：

• GDP per capita: in terms of Purchasing Power Parity (PPP) adjusted to constant 2011 international dollars.

  人均GDP：根據購買力平價(PPP)調整為2011年不變美元。

• Healthy life expectancy at birth.

  出生時的健康預期壽命 。

Happiness metrics:

幸福指標：

Happiness indicators mainly come from the Gallup World Poll (GWP), which continually surveys residents of different countries using randomly selected, nationally representative samples. These indicators are the following:

幸福感指標主要來自G allup世界民意測驗(GWP)， 繼續使用隨機選擇的具有國家代表性的樣本對不同國家的居民進行調查。 這些指標如下：

• Cantril Scale, or Life Ladder: it consists of asking respondents to rate their lives on a “ladder” scale ranging from 0 to 10, where 0 means the worst possible life.

  Cantril量表或生命階梯 ：它包括要求受訪者以0到10的“階梯”量表對他們的生活進行評分，其中0表示可能的最壞生活。

• Positive affect: it is the average of previous-day affect measures for happiness, laughter, and enjoyment.

  正面影響 ：這是前一天對幸福，笑聲和享受的平均影響程度。

• Negative affect: it represents the average of previous-day affect measures for worry, sadness, and anger.

  負面影響 ：它表示前一天擔心，悲傷和憤怒的平均影響程度。

Social indicators:

社會指標：

Social indicators also come from GWP surveys. They include:

社會指標也來自全球升溫潛能值調查。 它們包括：

• Social support: it represents the national average of the binary responses (either 0 or 1) to the question “If you were in trouble, do you have relatives or friends you can count on to help you whenever you need them, or not?”

  社會支持 ：它代表對問題“如果有麻煩，您是否有親戚或朋友可以依靠，無論何時需要，都可以幫助您”的二元答復的全國平均值(0或1) 。

• Generosity: it is the residual of regressing the national average of GWP responses to the question “Have you donated money to a charity in the past month?” on GDP per capita.

  慷慨大方 ：對“您在過去一個月是否向慈善機構捐款了嗎？”這一問題，對全球升溫潛能值React的全國平均值進行了回歸。 人均GDP。

• Freedom to make life choices: it represents the national average of binary responses to the question “Are you satisfied or dissatisfied with your freedom to choose what you do with your life?”

  做出生活選擇的自由 ：它代表對“ 您是否對選擇自己的生活做選擇的自由感到滿意或不滿意 ”的二進制答案的全國平均水平。

• Perceptions of corruption: it represents the national average of binary answers to two questions: “Is corruption widespread throughout the government or not?” and “Is corruption widespread within businesses or not?”

  對腐敗的看法 ：它代表對以下兩個問題的全國平均答案： “腐敗是否在整個政府中廣泛存在？” 和“ 腐敗在企業內部是否普遍存在？ ”

2.“經典”方法 (2. ‘Classical’ Approach)

2.1。 選擇變量 (2.1. Selection of Variables)

The first question I had to address is: what variables to keep for the modeling of happiness? In order words, what variables really matter in explaining Happiness?

我必須要解決的第一個問題是：為幸福建模留哪些變量？ 順便說一句，什么變量在解釋幸福方面真正重要？

For this purpose, I performed a Principal Component Analysis (PCA). This method extracts the most important information from data by constructing a smaller number of representative variables that collectively explain most of the variability in the original set.

為此，我進行了主成分分析 (PCA)。 該方法通過構造較少數量的代表變量來共同從原始數據集中解釋大多數變量，從而從數據中提取最重要的信息。

The new variables, called Principal components, are directions in feature space along which the original data is highly variable. Therefore, by analyzing their composition, it is possible to determine the variables to keep for the study.

新的變量稱為P主成分，是特征空間中原始數據高度可變的方向。 因此，通過分析其組成，可以確定要保留用于研究的變量。

For more information about PCA, you can read this article.

有關PCA的更多信息，您可以閱讀本文 。

The graph below shows the percentage of variance explains by each principal component. The two first ones explain most of the variance.

下圖顯示了每個主成分說明的差異百分比。 前兩個解釋了大部分差異。

The two graphs below analyses the constitution of the principal components and their correlation to the original variables.

下面的兩個圖形分析了主要成分的構成及其與原始變量的相關性。

The graphs strongly suggest that there are 6 key variables to keep in the modeling: GDP per capita, Social support, Healthy life expectancy at birth, Freedom to make life choices, Generosity, and Perception of corruption. Taken together, these six variables explain most of the variation in national annual average ladder scores among countries.

圖表強烈暗示了模型中應保留6個關鍵變量： 人均GDP，社會支持，出生時的健康預期壽命，自由選擇生活，慷慨大方和腐敗感。 綜上所述，這六個變量解釋了各國之間國家年度平均階梯得分的大部分差異。

Furthermore, it is possible to visualize how strongly each variable influences the two first principal components in a biplot. This graph also shows the correlation between variables through the angles between their representative vectors: the lower the angle between is the more the variables are positively correlated.

此外，可能的可視化每個變量如何強烈地影響在一個雙標圖兩個第一主成分。 此圖還通過變量代表矢量之間的角度顯示了變量之間的相關性：角度越小，變量之間的正相關性就越高。

Therefore, Life Ladder, GDP per capita, Healthy life expectancy at birth, and Social Support explains most of the first principal component and are strongly correlated to each other.

因此， 生活階梯 ， 人均GDP ，出生時的健康預期壽命和社會支持解釋了大多數第一主要要素，并且它們之間具有很強的相關性。

2.2。 幸福的模型 (2.2. Modeling of Happiness)

Correlations are useful to get quick insights about data. But, things can get tricky when it comes to identifying whether the correlation between two or more variables represents a causal relationship.

關聯對于快速了解數據很有用。 但是，要確定兩個或多個變量之間的相關性是否代表因果關系，事情可能會變得棘手。

Let’s take a famous example. In 2012, Messerli published a paper where he pointed out the high correlation between a country’s level of chocolate consumption and its population’s cognitive function. Does it mean that eating more chocolate would make you smatter? Unfortunately, probably not! For more information about causality, you can read this article or watch the video below.

讓我們舉一個著名的例子。 2012年，梅塞利(Messerli)發表了一篇論文 ，指出了一個國家的巧克力消費水平與其人口的認知功能之間的高度相關性。 這是否意味著多吃巧克力會使您感到不舒服？ 不幸的是，可能不是！ 有關因果關系的更多信息，您可以閱讀本文或觀看下面的視頻。

And yet, establishing causal relationships is crucial in decision making. For instance, countries with a high Healthy life expectancy at birth tend to be happier on average. Does it mean that ensuring a good healthcare system would increase people happiness? It depends as healthy people can still badly evaluate their life.

然而，建立因果關系對于決策至關重要。 例如， 出生時健康預期壽命高的國家通常會更快樂。 這是否意味著確保良好的醫療體系會增加人們的幸福感？ 這取決于健康的人仍然無法正確評估他們的生活。

Therefore, to answer these kinds of questions, it is necessary to use statistical tools, such as regression analysis. Regressions are often used by economists. They enable them not only to quantify the relationship between one variable and the other variables but also its relevance relationships through statistical tests.

因此，要回答此類問題，必須使用統計工具，例如回歸分析。 經濟學家經常使用回歸。 它們使他們不僅可以量化一個變量與其他變量之間的關系，還可以通過統計檢驗量化其相關性。

方法 (Methodology)

When performing a regression, it is important to control, on the one hand, for variables that are constant across countries but vary over time. For example, economic crises, such as the subprime crisis in 2008, had an impact on people's happiness globally.

進行回歸分析時，一方面，重要的是要控制各個國家之間恒定但隨時間變化的變量。 例如，經濟危機(例如2008年的次貸危機)對全球人們的幸福感產生了影響。

On the other hand, it is essential to control for time-invariant unobserved individual characteristics, such as the country weather. These controls enable us to really capture the causal relationships between the explanatory variables and happiness.

另一方面，必須控制隨時間變化的未觀察到的個人特征，例如鄉村天氣。 這些控制使我們能夠真正掌握解釋變量與幸福之間的因果關系。

To do so, I relied on the well-known technique of fixed effects. More specifically, I considered 3 settings depending on the fixed effects included in the regression.

為此，我依靠眾所周知的固定效果技術。 更具體地說，我根據回歸中包括的固定效果考慮了3種設置 。

1. Year effects
   年效應
2. Year and Regional effects
   年份和區域影響
3. Year and Country effects
   年和國家影響

This approach is similar to the one carried out in The World Happiness Report, except the fact that I rescaled the variable through a min-max normalization. This explains the difference in the results.

這種方法與《世界幸福報告》中執行的方法類似，不同之處在于我通過最小-最大規格化對變量進行了重新縮放。 這解釋了結果的差異。

結果 (Results)

Unsurprisingly, all the variables are significant under the 3 scenarios. More precisely:

毫不奇怪，在這三種情況下，所有變量都是顯著的。 更確切地說：

• Log GDP per capita is consistently the most important factor with a coefficient value ranging from 0.29 to 0.99.

  對數人均GDP一直是最重要的因素，系數值在0.29到0.99之間。

• Social support comes in the first position in the first scenario and the second position in the two others, with a coefficient value between 0.21 and 0.29.

  社會支持在第一種情況下排在第一位，在其他兩種情況下排在第二位，系數值在0.21和0.29之間。

• Healthy life expectancy at birth is only significantly different from 0 when considering the variance in the first scenario. It signs is even negative in the third scenario. This suggests that the results of the second scenario are the most reliable.

  當考慮第一種情況的方差時，出生時的健康預期壽命僅與0顯著不同。 在第三種情況下，這種跡象甚至是負面的。 這表明第二種情況的結果是最可靠的。

• Generosity and Perception of corruption are relatively less important and their variance is high.

  慷慨大方和腐敗感相對不太重要，并且差異很大。

3.機器學習方法 (3. Machine Learning Approach)

Over the past decade, the field of Machine Learning has known an important success. It has been applied to many areas and has proven to be very efficient, often outperforming usual statistical methods.

在過去的十年中， 機器學習領域取得了重要的成功。 它已應用于許多領域，并被證明是非常有效的，通常優于常規的統計方法。

However, research first has focused on developing the most performant algorithms in terms of accuracy of prediction or classification. It is only in recent years that it has shifted towards the need for establishing causal interference. Today, it is a great source of enthusiasm within the community of data scientists.

但是，研究首先集中在開發預測或分類的準確性方面性能最高的算法。 只是在最近幾年，它才轉向建立因果干擾的需要。 如今，它已成為數據科學家社區中熱情的重要來源。

In this context, I decided to apply the state-of-the-art interpretation techniques used in Machine Learning to get a better understanding of happiness drivers.

在這種情況下，我決定應用機器學習中使用的最新解釋技術，以更好地了解幸福驅動因素。

方法 (Methodology)

To do so, I proceeded in 4 steps:

為此，我分四個步驟進行：

a. Modeling of the national average happiness: I tested different Machine Learning algorithms on the dataset and fine-tuned their hyperparameters. b. Comparison of the relative importance of variables: I computed the relative importance of each variable using the best model.c. Analysis of the marginal impact of the variables on happiness: Go further by analyzing the partial dependence of explanatory variables on happiness.d. Analysis of happiness dynamics by region: Refine the analysis by taking a closer look at the region level.

一個。 全國平均幸福度建模：我在數據集上測試了不同的機器學習算法，并對它們的超參數進行了微調。 b。 變量相對重要性的比較：我使用最佳模型計算了每個變量的相對重要性。 C。 分析變量對幸福的邊際影響：通過分析解釋變量對幸福的部分依賴性，進一步分析。 d。 按區域分析幸福動態：通過仔細研究區域級別來完善分析。

The explanatory variables include the 6 key indicators (GDP per capita, Social support, Healthy life expectancy at birth, Freedom to make life choices, Generosity, and Perception of corruption) as well as year and regional fixed effect. These variables are rescaling via a max-min normalization as done previously.

解釋性變量包括6個關鍵指標( 人均GDP，社會支持，出生時的健康預期壽命，自由選擇生活，慷慨大方和腐敗感) 以及年度和區域固定效應。 如前所述，這些變量通過最大-最小歸一化進行縮放。

I used the following Python libraries: scikit-learn and skater.

我使用了以下Python庫： scikit-learn和skater 。

結果 (Results)

a. Modeling of the national average happiness

一個。 全國平均幸福度建模

I applied the most frequently used Machine Learning algorithms to predict Life Ladder based on the explanatory variables. To compare their performance in terms of prediction, I performed a 5-fold cross-validation and compared the mean Root Mean Square Error (RMSE).

我根據解釋變量應用了最常用的機器學習算法來預測“ 人生階梯” 。 為了比較它們在預測方面的性能，我進行了5次交叉驗證，并比較了均方根誤差(RMSE) 。

The results represented in the graph below suggest that tree-based methods exhibit better results. More especially, Extra Trees algorithm presents the lowest RMSE.

下圖所示的結果表明基于樹的方法顯示出更好的結果。 更特別地， Extra Trees算法呈現最低的RMSE 。

b. Comparison of the relative importance of variables

b。 變量相對重要性的比較

Extra-Trees is a well-known algorithm that trains multiple randomized decision trees and combines them by averaging their results. The graph briefly explains the underlying principle and the step of this algorithm.

Extra-Trees是一種眾所周知的算法，它訓練多個隨機決策樹并通過對它們的結果取平均來組合它們。 該圖簡要說明了該算法的基本原理和步驟。

More information about forests of randomized trees is provided in sckit-learn documentation, here.

關于隨機樹木的森林中提供更多信息sckit學習文檔， 在這里 。

Extra Trees model, as a tree-based model, provides an interpretation of its results through the importance of features. These are computed as the decrease in the impurity of each node where the feature is present, weighted by the probability of reaching this node.

額外的樹木模型，基于樹的模型，通過提供功能的重要性及其結果的解釋。 將這些值計算為存在該特征的每個節點的雜質減少量，并按到達該節點的概率進行加權。

The graph below represents the feature importance of the variables as given by the model. Log GDP per capita, Social support and Healthy life expectancy at birth appears to be the most determinant factor of Life Ladder. This is not the case of the other models, namely Random Forest, AdaBoost and Gradient Boosting. These algorithms place Healthy life expectancy at birth before Log GDP per capita and Social support.

下圖顯示了模型給出的變量的特征重要性。 原木人均GDP ， 社會支持和出生時健康的預期壽命似乎是決定人生階梯的最重要因素。 其他模型( 隨機森林，AdaBoost和梯度增強)則不是這種情況。 這些算法將出生時的健康預期壽命放在 人均GDP和社會支持之前。

c. Analysis of the marginal impact of the variables on happiness

C。 變量對幸福的邊際影響分析

It is also possible to visualize the marginal impact of each of these 3 variables on the model predictions by plotting partial dependencies. The graphs below show a slight upward trend. This means that an increase of one variable among Log GDP per capita, Social support and Healthy life expectancy at birth, while holding other variables in the model constant, leads to an increase of happiness.

通過繪制部分相關性，還可以可視化這三個變量中的每一個對模型預測的邊際影響。 下圖顯示了輕微的上升趨勢。 這意味著，在人均GDP不變， 社會支持和健康出生時預期壽命之間增加一個變量 模型常量中的其他變量會導致幸福感增加。

The analysis can be taken one step further by visualizing the marginal impact of two variables on the model predictions. The 3D graph below is consistent with what we could have expected: the higher one’s wealth and social support are, the happier he is!

通過可視化兩個變量對模型預測的邊際影響，可以進一步進行分析。 下面的3D圖與我們可以預期的一致：財富和社會支持越高，他就越快樂！

On the whole, the analysis conducted so far not only confirms the insights we have seen by manipulating the data but also allows us to quantify them. Money and health with the social support of our loved ones are the pillars of happiness. They are the factors that drive people to evaluate their lives positively.

總體而言，到目前為止進行的分析不僅可以通過處理數據來確認我們已經看到的見解，還可以量化這些見解。 金錢和健康在我們親人的社會支持下是幸福的Struts。 它們是驅使人們積極評價自己生活的因素。

Nevertheless, these observations are made on a worldwide scale. We still need to explore happiness dynamics from a country perspective to make new discoveries.

然而，這些觀察是在全球范圍內進行的。 我們仍然需要從國家的角度探索幸福的動態，以發現新的發現。

d。 按地區分析幸福動態 (d. Analysis of happiness dynamics by region)

The analysis becomes even more interesting when considering the country level by geographical region. In particular, there is a significant gap between developed countries, emerging countries, and developing countries. These countries do not value things in the same way. Let’s take a look!

當按地理區域考慮國家/地區級別時，分析變得更加有趣。 特別是， 發達國家，新興國家和發展中國家之間存在巨大差距。 這些國家不以相同的方式重視事物。 讓我們來看看！

North America

北美

The results for North American countries are the most surprising and radically different from the rest: Log GDP per capita lags behind other factors. Its importance barely represents half of the importance of Freedom to make life choices. Healthy life expectancy at birth, Social support, and Perception of corruption come after with a relatively similar importance in the model prediction of happiness.

北美國家的結果是最令人驚訝的，并且與其他國家截然不同： 人均原木GDP落后于其他因素。 它的重要性僅代表自由做出生活選擇的重要性的一半。 隨之而來的是出生時的健康預期壽命，社會支持和腐敗感 在幸福的模型預測中具有相對相似的重要性。

The partial dependence graphs of Log GDP per capita, Social support and Healthy life expectancy at birth show a growing trend towards flattening. This suggests that after a certain point, an increase in their value does not lead to a significant increase in happiness.

人均GDP的對數，社會支持和出生時的健康預期壽命的偏倚圖顯示出趨于扁平化的趨勢。 這表明，在一定程度上，他們的價值增加并不會導致幸福感的顯著增加。

For Western European countries, Log GDP per capita and Perceptions of corruption play a similar role in determining people happiness. Again, Freedom to make life choices comes in the third position, just before Social support. On the contrary, Healthy life expectancy at birth lags behind other variables.

對于西歐國家來說， 人均GDP的對數和對腐敗的看法在確定人們的幸福感方面起著相似的作用。 再者， 做出生活選擇的自由排在第三位，就在社會支持之前。 相反， 出生時的健康預期壽命落后于其他變量。

As for North American countries, the partial dependence graph of Log GDP per capita shows a growing trend towards flattening which suggests that after a certain point, an increase of wealth does not lead to a significant increase of happiness.

對于北美國家而言， 人均GDP的對數偏倚關系圖顯示出趨于扁平化的趨勢，這表明在一定點之后，財富的增加并不會導致幸福感的顯著增加。

For emerging and developing countries, Log GDP per capita is, consistently and by far, the most important factor. The variable that comes next depends on the region, usually Social support or Healthy life expectancy at birth. In the case of South Asian countries, Social support is almost as important as Log GDP per capita.

對于新興國家和發展中國家， 人均GDP一直是迄今為止的最重要因素。 接下來的變量取決于地區，通常是社會支持或出生時的健康預期壽命。 在南亞國家， 社會支持幾乎與人均GDP一樣重要。

Even more surprisingly is the partial dependence on the Log GDP per capita which has a bell shape. This would suggest that, after a certain level of wealth, an increase in one’s wealth would cause a degradation of his happiness!

更令人驚訝的是，部分依賴于人均GDP呈鐘形。 這表明，在一定水平的財富之后，一個人的財富增加會導致他的幸福感下降！

Social support is also the second most important variable of countries in Central and Eastern Europe, Sub-Saharan Africa, Commonwealth of Independent States, but not always with the same relative proportion, as shown in the graphs below.

社會支持也是中歐，東歐，撒哈拉以南非洲，獨立國家聯合體國家的第二重要變量，但并非總是相對比例相同，如下圖所示。

On the contrary, countries in the Latin America and Caribean, Middle East and North Africa East, East and Southeast Asia ‘value’ more Healthy life expectancy at birth than Social support, as suggested in the graph below.

相反，如下圖所示，拉丁美洲和加勒比海地區，中東和北非地區的東，東和東南亞國家“重視” 出生時的健康預期壽命而不是社會支持 。

How to explain these differences between countries?

如何解釋國家之間的這些差異？

Some might say it’s all about countries' culture and values but actually it is a tricky question that needs a deeper study. Nevertheless, the analysis undertaken already gives us an idea of what people in a country value the most and what policies should be introduced to improve their living conditions.

有人可能會說這全都與國家的文化和價值觀有關，但實際上這是一個棘手的問題，需要深入研究。 盡管如此，進行的分析已經使我們了解了一個國家的人們最看重什么，應該采取什么政策來改善他們的生活條件。

局限性 (Limitations)

Finally, I would like to point out 3 main limitations of the approaches presented above:

最后，我想指出上述方法的三個主要局限性：

• Omitted variables: Although intuitively relevant given the topic, the variables used to explain happiness might not be enough. Their correlation might actually reflect some other “unobserved” factor that is not included in the analysis.

  省略的變量：盡管給定主題在直觀上相關，但用于解釋幸福的變量可能還不夠。 它們之間的相關性實際上可能反映了分析中未包括的其他“不可觀察”因素。

• Reverse causality: There is also a risk of bidirectional causality. This means that happiness can cause changes in one or more explanatory variables. For instance, are people happy because they are healthy, or is their sentiment of happiness that makes them feel healthy? Are people happy because they are wealthy or is the feeling of happiness that makes them more dynamic and ambitious in their professional lives?

  反向因果關系：還存在雙向因果關系的風險。 這意味著幸福會導致一個或多個解釋變量發生變化。 例如，人們是因為健康而快樂，還是使自己感到健康的幸福感？ 人們是因為自己有錢而幸福，還是因為幸福感使他們的職業生活更加充滿活力和野心？

• Mismeasurement: Many variables analyzed are subjective and represent more people perceptions than reality. For example, people from a country with a long political tradition of democracy might feel corruption more strongly while it remains weaker and less widespread than in other countries. Moreover, choosing GDP per capita and Healthy life expectancy at birth to represent respectively people wealth and health.

  錯誤計量：分析的許多變量都是主觀的，代表的是人們對現實的認識多于現實。 例如，來自一個有著悠久民主政治傳統的國家的人們可能會比其他國家更強烈地感受到腐敗，而它仍然比其他國家更弱小和普遍。 此外，選擇人均GDP和出生時的健康預期壽命分別代表人民的財富和健康。