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2 Statistical Data Analysis by STATA For Social Researchers 2 <Advanced Part 1 >. Text 6.. Regression Analysis Structural Equation Modeling 1 (Regression) Structural Equation Modeling 2 (Use of Latent Variable) Version 2.2 (February 04, 2013) Ryo SASAKI Ph.D. 1 Advanced part is also available. It consists of (i) Difference in Difference (DID), (ii) Propensity Score Matching (PSM), and (iii) Instrumental Variable (IV).

3 <How to obtain STATA trial version> Please apply to obtain a trial version of STATA at the following site. i

4 Data Analysis by STATA for Social Researchers 2 Advanced Part Table of Contents Session 4:Regression Analysis 1 Session 5:Structural Equation Modeling 1 (Regression) 13 Session 6:Structural Equation Modeling 2 (Use of Latent Variable) 23 Special Session:Making and Using Do-File 36 Author 38 Revision History 39 ii

5 Session4 Regression analysis: How much was the REAL effect of Your intervention? 1: Let s estimate the effect by comparing with your rival groups The government of city E introduced pay-trash-bag policy in order to reduce the volume of trash and garbage. (named PaTrash ). This policy requests the collection trucks to collect only the bags that are paid in advance. Other cities are watching how much this policy get successful at City E. Then, the volume of trash collected are recorded at major cities in this region. Can we say the volume of trash has been decreased by introduction of this new policy? <Necessary conditions> - The data of outcome indicators (in this case, Volume of trash ), the date of intervention indicators(in this case, PaTrash ), and other explanatory variables (in this case, Population ) are necessary. - No strong correlation between explanatory variables is necessary. 1

6 Input of data 1st column.name of town 2 nd column Population (,000people) 3 rd column Introduction of PaTrash (1=Yes, 0=No) 4 th column Volume of trash (tones) 2

7 Import of Data Select: File>Import>Excel spreadsheet(*.xls, *.xlsx). Select: File>Import>Excel spreadsheet (*.xls, *.xlsx). Then select the Excel file you made. In the box come up, give check to Import first row as variable names. Click OK. 3

8 Select: Data > Data Editor > Data Editor (Edit). (Alternatively, click the icon of Data editor )Confirm the data are correctly imported. (Click Format if you need to show a certain decimal points.) Select: Statistics > Linear models and related > Linear regression. 4

9 At Dependent variable, select Volume_trash. At Independent variable, select Population PaTrash. Click Reporting tab, and give check to Standardized beta coefficients. Click OK. 5

10 Obtain the analysis result The following result is obtained. The enlarged view is as follows You should check the four items. 1 R Square (R 2 ): How much changes the obtained equation explains. In this case, 87.63% is explained by the obtained equation. 2 F:It indicates the statistical significance of the whole equation. If its p-value (see Significance F) <0.05, it is statistically significant. 6

11 In this case, p-value is It is less than P-value of coefficients:it indicates the statistical significance of each variable. If p-value <0.05, it is statistically significant. In this case, all two variables, as well as the cut-off, are judged as statistically significant. 4 Coefficients: It indicates how much each variable can explain the change in the outcome variable (in this case Volume of trash ). In this case, volume of trash increases by if 1,000 people increases. Also the volume of trash decreases by 1, tones by introduction of PaTrash. Volume of trash= (population) ( PaTrash ) Result of Analysis In this case, it can be concluded that the volume of trash decreased by introduction of the pay-trash-bag policy ( PaTrash ). The volume decreased by this policy is estimated as 1,914 tones. Since the volume of trash in the case that this policy be not introduced is calculated as 3,433 tones, about 56% of reduction was realized. ( (7.2) (0) = 3,433 ) By the way, the strong correlation between volume of trash and population is observed and it is confirmed statistically significant. Thus, it is expected that the increase of the volume of trash along with the increase of population is expected. (Note) A scatter plots like the following page would help readers understanding. It is also recommended to add a regression line (that should be drawn by hand on the chart). 7

12 It is estimated that the new policy ( PaTrash ) made the volume of trash decreased at town E by 1,914 tones. 8

13 Select: Graphics > Twoway graph (scatter, line, etc.). Select Create. At Y variable, select Volume_Trash. At X variable, select Population. Click Accept. 9

14 Confirm Plot 1 appears, and click OK. The following scatter plot figure appears in a new window. Click Start Graph Editor 10

15 Click the scale of Y axis.> Click Scale > At Lower limit, type 0.>Click OK. Now Y axis starts from 0. Then, add title, note and others using this box. 11

16 (Advanced study: How to understand Standardized Coefficient) Since you give a check to タブで Standardized beta coefficients at Reporting tab, the standardized coefficients (named Beta ) are also calculated. Kline(2005, p.122)proposed the generalized criteria for standardized coefficient based on 標 the proposal of Cohen(1988). However, Cohen stated it is risky to propose an generalized criteria, and Kline also stated these criteria should be used as temporary one at the areas where subject-matter knowledge has not been enough accumulated. If the standardized path coefficient is less than0.1, it is small effect. If it is more or less 0.3, it is medium effect. If it is more than 0.5, it is large effect. (Source) Kline, R.B. (2005). Principles and practice of structural equation modeling (2 nd ed.).new York, NY: The Guilford Press 12

17 Session 5 Structural Equation Modeling 1(Multiple 1 regression) <We analyze the same case of Session 4 by using Structural Equation Modeling (SEM)) The government of city E introduced pay-trash-bag policy in order to reduce the volume of trash and garbage. (named PaTrash ). This policy requests the collection trucks to collect only the bags that are paid in advance. Other cities are watching how much this policy get successful at City E. Then, the volume of trash collected are recorded at major cities in this region. Can we say the volume of trash has been decreased by introduction of this new policy? The following figure is the image of SEM of PaTrash. 13

18 Input of data 1st column.name of town 2 nd column Population (,000people) 3 rd column Introduction of PaTrash (1=Yes, 0=No) 4 th column Volume of trash (tones) 14

19 Import of data Select: File>Import>Excel spreadsheet(*.xls, *.xlsx). Select: File>Import>Excel spreadsheet (*.xls, *.xlsx). Then select the Excel file you made. In the box come up, give check to Import first row as variable names. 15

20 Select: Data > Data Editor > Data Editor (Edit). (Alternatively, click the icon of Data editor )Confirm the data are correctly imported. (Click Format if you need to show a certain decimal points.) Select: Statistics > SEM(structural equation modeling) > Model building and estimation. 16

21 The following empty canvas will appear. First, draw three quandrangles. Next, draw a arrow. Then, automatically an error variable ( e1 ) is added. 17

22 Next, draw a second arrow. Next, draw a line of which both ends are arrows. Draw a line from the lower quadrangle to the upper quadrangle. Click each quandrangle and select an appropriate name for each. 18

23 Select: File > Save As At the box appeared, give a name and click Save. Select: Estimation > Estimate 19

24 Click Reporing tab. At Reporting tab, give check to Display sandardizd coefficients and values. Click OK. The calculation result will appear. 20

25 Some numbers look very strange (e.g., 2.6e +02). In that case, click the box in the right paine. Then you can see the accurate numbers. Now you can write an equation using those accurate numbers. Y = pop trashbag Compare the output of SPSS AMOS. They are totally same. 21

26 Select: View > Standardized Estimates. You can see the standardized coefficients. Again, compare the output of SPSS AMOS (Standardized values). They are totally same. Commonly used criteria for judging size of standardized coefficients is as follows. (Cohen(1988), Kline(2005)) If the standardized path coefficient is less than0.1, it is small effect. If it is more or less 0.3, it is medium effect. If it is more than 0.5, it is large effect. 22