群體差異比較：以生命表的統計推論爲例

Group Differences Comparison: Application of Bootstrap Approach to the Statistical Inference for Life Table Analysis

陳信木(Hsin-Mu Chen)

《調查研究-方法與應用》 16期 (2004/10) Pp. 37-71

https://doi.org/10.7014/TCYCFFYYY.200410.0037

摘要

群體之間的差異(group difference)，乃是社會研究的核心焦點；尤其，近來對民生命歷程發展的關注，更是強調探討不同群體之間的社會行爲差異。現在，社會研究大量援用樣本(sample)實證資料，因此，立基於樣本資料所發現之群體差異經驗的結果，如果試圖概化至母體(population)時，必須運用適切的統計推論知識。樣本推論自體的知識，在抽樣調查研究領域已經高度成熟發展，所以社會研究者進行群體差異比較推論時，可以適切仰賴這些成熟的理論知識。然而，近年來社會研究領域內一些新的發展趨勢，卻使得此一局面產生變化，進而衍生若干統計推論上的困境。基於這些和當前社會研究發展趨勢考量，本文試圖以「生命表函數之統計推論」爲例，探討應用再抽樣遠徑(resampling approach)進行非參數式之統計推論的可能策略，作爲根據樣本發現推論母體之群體差異經驗的可行方法。
生命表方法已經是人口研究的標準工具，而且現在生命表方法更是廣泛應用至不同的研究議題上，目的不僅只是探討群體的存活經驗，研究者經常更是希望比較群體之間存活經驗的風險差異。因此，生命表的統計推論需求必然更加迫切。在本文中，我們引用Bootstrap再抽樣方法作爲生命表函數比較的途徑，從實證分析的結果來看，Bootstrap的確相當合適設作爲生命表面數比較的工具。其次，在此可以發現，即使是類似生命表此種成熟發展的分析工翼，也會面臨統計推論困境。那麼社會研究試圖比較群體差異時，其所援用的統計分析工具或是樣本實證資料，可能遭遇更爲困難的局面。在此狀況之下，類如本文使用的Bootstrap再抽樣模擬途徑，或是其他的非參數式統計推論策略，就是很好的解決方案之一。

關鍵字

群體差異 ； 生命表方法 ； 非參數式統計推論 ； 再抽樣 ； Bootstrap模擬 ； 多重遞增遞減生命表

並列摘要

Group differences have been a major focus in social research Typically, group differences are based solely on comparisons of expectancies, i.e., the expected pattern of behavior for the average individual in a group. Because these comparisons are substantive and not statistical, questions of whether groups are statistically different in their life course behavior patterns remain unanswered. Nowadays, sociological findings for group differences are typically derived from large and nationally representative samples. Sampling variability is thereby introduced into the behavior model.
Moreover, social studies usually employ complex samples that make the traditional statistical inference procedures impossible. This calls for a new strategy to evaluate group differences statistically. Here, we describe one approach to statistically evaluate group differences. This approach allows researchers to estimate both the expected values and the variances for complex samples, thereby permitting formal statistical tests for group differences. We demonstrate this approach by using a multistate life table model. Traditionally, multistate life model operates at the population-level. Hence, we see the lack of attention to variability in the life table functions. Increasingly, however, demographers apply multistate life table methods to studies employing national complex samples. With the assistance of the approach we describe here, even the multistate life table method could be possibly applied to evaluate group differences.

並列關鍵字

Group Differences ； Life Table Method ； Resampling ； Increment-life Table ； Bootstrap Approach ； Statistical Inference

參考文獻

Akritas, Michael G.(1986).Bootstrapping the Kaplan-Meier Estimator.Journal of the American Statistical Association.81(396),1032-1038.

Andersson, Claes,Goosta Forsman,Jan Wretman(1987).Estimating the Variance of a Complex Statistic: A Monte Carlo Study of Some Approximate Techniques.Journal of Official Statistics.3(3),252-265.

Avery, Roger C.(1973).Patterns and Implications of Long-Term IUD Use in Taichung, Taiwan.Studies in Family Planning.4(6),139-143.

Bartholomew, David J.,Panagiota Tzamourani(1999).The Goodness of Fit of Latent Trait Models in Attitude Measurement.Sociological Methods and Research.27(4),525-546.

Bellhouse, D. R.(1985).Computing Methods for Variance Estimation in Complex Surveys.Journal of Official Statistics.1(3)