Effective Approaches to Detect Manifest Moderating Effects on the Construct Relationships
Cherng G. Ding
|關鍵字:||調節變數;factor-based scores;factor scores;調節迴歸分析法;檢定力;Moderators;factor-based scores;factor scores;Moderated Regression Analysis(MRA);Power|
|摘要:||在社會科學的領域上，許多的研究常會涉及到不可直接觀察心理構念的衡量與這些構念間關係的研究，因此線性結構模式 (structural equation modeling, SEM) 在行為科學的應用上日趨普及。此外，我們常會引進影響到自變數與依變數之間關係的調節變數 (moderator)，不管它是屬性(例如性別、種族、等級等)或是屬量(例如年齡、所得、年資等)的社會經濟變數。以往學者為了簡單方便常採用factor-based score 的方法估算構念分數，也就是將衡量構念所有項目的分數予以加總求得平均分數，然而此法卻忽略了構念項目的權重的問題。此外依據文獻所示，採用驗證型因素分析(Confirmatory Factor Analysis) 所得到的因素分數來估算構念分數可降低衡量誤差的扭曲效果。本研究在傳統的調節迴歸分析法 (Moderated Regression Analysis, MRA)下，探究不同構念分數估計方法是否可提高構念間關係之類別外顯調節效果檢定之檢定力。另外，針對連續外顯調節效果檢定，本研究提出一修正的調節迴歸分析法(Modified MRA)，並與傳統調節迴歸分析法以蒙地卡羅模擬進行檢定力與偏誤之大小比較。
本研究針對以factor-based scores 為基礎之傳統MRA法（以下簡稱方法A）、以CFA 所得之factor scores 為基礎之傳統MRA法（以下簡稱方法B）、以factor-based scores 為基礎之修正MRA法（以下簡稱方法C）以及以CFA 所得之factor scores 為基礎之修正MRA法（以下簡稱方法D）等四種方法進行調節效果檢定之檢定力與估計偏誤之大小比較。另一方面，鑒於實務上研究者常將連續調節變數以中位數或平均數的方式轉換成類別調節變數，此舉對於前述之檢定力與估計偏誤的影響為何亦是本研究討論的重點。
針對連續調節變數而言，當調節效果不存在時，前述A、B、C、D四種方法所得之檢定力均接近顯著水準。當外生構念與內生構念衡量項目之因素負荷量皆呈現明顯差異時，檢定力大小比較結果為：D > B > C > A。當僅有內生構念衡量項目之因素負荷量呈現明顯差異時，檢定力比較結果為：D □ B □ C > A。當僅有外生構念衡量項目之因素負荷量呈現明顯差異時，檢定力比較結果為：D □ B > C □ A。當外生構念與內生構念衡量項目之因素負荷量皆無明顯差異時，則檢定力比較結果為：D □ B □ C □ A。此外，若將連續調節變數轉換成類別調節變數，將造成檢定力明顯降低。至於在偏誤的衡量上，我們發現上述四種方法的平均標準誤差都非常接近，然而使用不同的因素分數以及是否採用修正MRA法會導致統計檢定力有差異。使用以CFA 所得之factor scores 為基礎或是修正MRA法都可以改善衡量誤差對於調節變數估計參數有偏低誤差的情形。然而，若將連續調節變數轉換成類別調節變數後，將會嚴重的使偏誤加大。因此在檢測構念間的調節效果時應避免類別化。
根據本研究所獲得的結果，我們建議針對類別調節變數，以CFA 所得之factor scores 為基礎之傳統MRA法來檢測構念間的調節效果，可以明顯的提昇統計檢定力。針對連續調節變數，以CFA 所得之factor scores 為基礎之修正MRA法來檢測構念間的調節效果，可以明顯的提昇統計檢定力。|
In behavioral studies, involving unobserved directly constructs the structural equation modeling (SEM) technique has become popular. Socioeconomic variables are often introduced as moderators. A moderator, in general terms, is a categorical (e.g. sex, race, class) or continuous (e.g. age, income, tenure, work experience) variable that affects the relation between an independent variable and a dependent variable. Factor-based scores are the most commonly used scores for latent factors. With the factor-based scoring approach, two or more attributes measuring a common underlying construct are summed up and divided by the number of the items. However, this method ignores the weights of the measurement items. In addition, literature review reveals that the use of factor scores derived from CFA could reduce the distorting effects from the measurement errors on coefficient estimates. This study explores whether different scoring approaches could increase the power of the categorical manifest moderating effects or not. In addition, a modified moderated regression analysis (modified MRA) is proposed to detect moderating effects for continuous manifest moderators in structural equation modeling (SEM). We use Monte Carlo simulation to compare the power and the bias associated with the moderating effect resulting from traditional MRA and modified MRA. The power and the bias are compared among the four different approaches: traditional MRA with factor-based scores (approach A), traditional MRA with factor scores derived from CFA (approach B), modified MRA with factor-based scores (approach C), and modified MRA with factor scores derived from CFA (approach D). On the other hand, loss of power and bias information due to categorizing continuous manifest moderator are also examined. For categorical moderators, the results indicated that when there is no moderating effect, the power resulting from factor-based scores and factor scores derived from CFA as the input of traditional MRA are both close to significance level. When there is a moderating effect, the power based on factor scores derived from CFA is substantially higher than that based on factor-based scores in the situations of different factor loadings. If the indicators of the same underlying construct have the same factor loadings, then the power based on the two scoring approaches is almost identical. For continuous moderators, the results indicated that when there is no moderating effect, the power resulting from the above-mentioned four approaches is close to significance level. If the factor loadings are substantially different (e.g., (0.9, 0.6, 0.5)) for both of the exogenous and endogenous constructs, then the ranking of the power performance is D > B > C > A. If the factor loadings are substantially different for the endogenous construct only, then the ranking of the power performance is D □ B □ C > A. If the factor loadings are substantially different for the exogenous construct only, then the ranking of the power performance is D □ B > C □ A. If none of the exogenous and endogenous constructs has substantially different factor loadings, then the ranking of the power performance is D □ B □ C □ A. Moreover, categorizing continuous manifest moderator will lead to substantial power loss. As for the bias assessment, we found that the mean standard errors for different approaches are quite similar; however, different scoring approaches and the modification of MRA can lead to power difference. The bias could be improved by either using factor scores derived fro CFA or the modified MRA in order to reduce the influence of measurement errors. Nevertheless, categorizing a continuous manifest moderator would seriously enlarge the bias. Therefore, categorization should be avoided before testing for moderating effects. According to our research results, for categorical moderator, we strongly suggest that researchers should use factor scores derived from CFA instead of factor-based scores as input for the traditional MRA to test for moderating effects on the relationships between constructs to increase statistical power; for continuous moderator, researchers should use factor scores derived from CFA for the modified MRA to test for moderating effects on the relationships between constructs to increase statistical power.