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business statistics using excel
Multiple Regression And Beyond 1st New International Edition Timothy Z. Keith - Solutions
=+a. Estimate the model as shown. Focus on the fit indexes and, if you judge them to be adequate, interpret the model.
=+LATENT VARIABLE MODELS: MORE ADVANCED TOPICS TABLE 5 Variable Names and Variable Labels for the Eisenberg and Colleagues Model VARIABLE NAME(EISENBERG ET AL 2001.XLS)Exp_mo Exp_msr Reg_mr Reg_tr Exter_mr Ext_tr Soc_mr Soc_tr VARIABLE LABEL (FROM FIGURE 22)Expressivity Observed Expressivity
=+The model is contained in the Amos file “Eisenberg et al 1.amw.” Simulated data designed to mimic the relevant portions of the correlation matrix presented in the article are contained within the Excel file “Eisenburg et al 2001.xls” and the SPSS file “Eisenburg et al 2001.sav”
=+2. Nancy Eisenberg and colleagues (2001) conducted research to determine the effects of mothers’ emotions on their young children’s behavior problems and social competence. One interest in the research was whether these effects are mediated by children’s own emotional regulation. Figure 22
=+c. Compare the model with the two competing models discussed in this chapter (the Direct Background Effects model and the No Homework Effect model).
=+b. Interpret the model. Be sure to interpret the indirect and total effects in addition to the direct effects.
=+a. Study the parameter estimates and standard errors, the fit statistics, modification indexes, and standardized residuals. Are there changes that you might make to the model? Are they theoretically justifiable?
=+1. If you have a full-featured SEM program, analyze the series of full homework models starting with the model shown in Figure 1. Make sure your results match those presented here. If you are using a student version of a program that places a limit on the number of variables you can analyze, try
=+d. Are there any common causes that the research may have neglected? How could you investigate the possibility of unmeasured common causes more completely?
=+c. Are there other alternative models that you are interested in testing? Are they equivalent to the initial model? Test these models; be sure to evaluate the relative fit of the model and to interpret your findings.
=+b. Fix the path from Head Start to Cognitive Ability to zero; compare the fit of this model to the initial model. Do you still come to the same conclusion as before?
=+a. Draw (set up) and estimate the model. Is the structural portion of the model just-identified or overidentified? Evaluate the fit of the model and, if adequate, focus on parameter estimates. Interpret the model. According to these results, does Head Start have a positive effect on cognitive
=+1 for those who participated in Head Start and 0 for children in the control group. The data are shown in Table 3. These are data from 303 children from an early Head Start evaluation, 148 who attended Head Start in the summer and 155 who did not. To understand why the example is so
=+2. Figure 13 shows a model to test the effects of participation in Head Start on children’s cognitive ability. This example is a classic reanalysis of a controversial quasi-experiment; I have seen variations of it presented in Kenny (1979) and Bentler and Woodward (1978), among others. The
=+e. Are there any common causes that the authors may have neglected? How could you investigate the possibility of unmeasured common causes more completely?
=+d. Are there other alternative models that you are interested in testing? Do so; be sure to evaluate the relative fit of the model and to interpret your findings.
=+c. Compare the initial model with the competing model discussed in this chapter (the Achievement Effect model). Do you agree that this model is a better alternative? What theoretical, logical, and research evidence can you offer in support of this model? What evidence argues against this model?
=+b. Interpret the model. Be sure to interpret the indirect and total effects in addition to the direct effects.
=+a. Estimate the models discussed in this chapter. Study the parameter estimates and standard errors, the fit statistics, modification indexes, and standardized residuals.
=+1. Analyze the simulated Buhs and Ladd data (“Buhs & Ladd data.sav” or Buhs & Ladd data.xls”) using a structural equation modeling program (if you are using Amos, the initial model is saved as “Buhs & Ladd model 1.amw”).
=+c. As you examine your analyses, are any other hypotheses or models suggested by the findings? If so, conduct these analyses and interpret the findings.
=+b. Note the fit indexes. Which changed the most from the analyses in the chapter? Why do you think this may be?
=+a. Conduct the first-order factor analyses from this chapter using the simulated data. Interpret the findings. How do the results compare with those in this chapter (and in Exercise 1)? Would you come to different conclusions following these analyses than we did in the chapter?
=+3. The files “DAS simulated.sav” and “DAS simulated.xls” include 500 cases of simulated data for the DAS.
=+First use SPSS (or another general statistical program) to create a matrix for analysis in Amos (or one of the other programs). Then analyze your model using this matrix.
=+2. The NELS data include a series of items (ByS44a to ByS44m) designed to assess students’self-esteem and locus of control. Choose several or all of these items that you believe best measure self-esteem and locus of control and subject them to confirmatory factor analysis.
=+1. Conduct the analyses outlined in this chapter. If you have a student version program that only allows a certain number of variables, you may be able to estimate a portion of the models. The Amos student version allows eight measured variables, which means you should be able to estimate all
=+How do they label the disturbances?The error and unique variances of the measured variables?
=+ Do they link latent variables with reliability and validity?
=+4. Find an article in your area of interest that uses latent variable structural equation modeling(it may be referred to as structural equation modeling or covariance structures analysis).Read the article. Do the authors discuss reasons for using latent over measured variables?
=+3. What is the advantage of moving from a measured to a latent variable approach? What might happen to the estimates of effects with this transition?
=+Think of ways to include multiple measures of the researchers’ independent and dependent variables. Draw a model incorporating both measured and latent variables.
=+2. How could you convert this research from a measured variable study into a latent variable study?
=+1. Pick a research study in your area of interest. Describe the latent variables, the constructs the authors were interested in. What was the construct of interest underlying the independent variable(s)? What was the construct of interest underlying the dependent variable(s)? What measured
=+ Compare the fit of the two models. What conclusions do you reach from these model comparisons?
=+6. Estimate the nonrecursive trust model from Figure 17. The model (trust nonrecursive model 1.amw) and the data (trust norec sim data.xls) are included on the accompanying Web site(www.ablongman.com/keith1e). Second, assume that the Man’s Trust affects his partner, but not the reverse: delete
=+ Test an alternative model to determine whether Family Relationships directly affect the outcome variables.(The Henry et al., 2001, article reported correlations among variables. The data used in this example were simulated data designed to mimic these correlations. The Family Relationships
=+Which variable was more important for boys’ violence? What were the indirect effects of Family Relationships on Individual’s Violence and Delinquency?
=+Data consistent with those reported in the original article are in the SPSS file “Henry et al.sav” or the Excel file “Henry et al.xls.” Analyze and interpret this model. Which variable had a more important effect on boys’ delinquency: peers who are delinquent or peers who are violent?
=+5. Henry, Tolan, and Gorman-Smith (2001) investigated the effect of one’s peers on boys’ later violence and delinquency. Figure 21 shows one model drawn from their study, their “fully mediated” model. Family Relationships is a composite of measures of family cohesion, beliefs about
=+4. Focus on the equivalent models in Figure 14. Note the difference between these and the initial model (model A). Which rule or rules were used to produce each equivalent model?Check your answers against those in note 5. Try estimating one or two of these models to demonstrate that they are
=+Previous Achievement to Grades to zero and check the fit of the model. Now delete that same path. Is the fit the same? Are the parameter estimates the same for the two models?!?2
=+3. In the section introducing overidentifying models, I stated that “not drawing a path is the same as drawing a path and fixing or constraining that path to a value of zero.” Demonstrate the truth of this statement. Using the homework model, constrain, for example, the path from
=+2. Try estimating a similar homework model using your NELS data.
=+1. Reproduce the Homework models used in this chapter. Make sure your results match mine(note there may be minor differences in estimates if you are using programs other than Amos). Are there additional models that you might test?
=+b. Did you draw a path from Self-Esteem to Locus of Control or Locus of Control to SelfEsteem? Calculate the direct, indirect, and total effects of these two variables on Social Studies Achievement. Whichever way you drew the path, now reverse the direction and reestimate the model. Recalculate
=+a. Notice the direct effects of Self-Esteem and Locus of Control on Social Studies Achievement. Focus on the effect of GPA on Self-Esteem and Locus of Control. Is 8thgrade GPA a common cause of these variables and Social Studies Achievement? Now remove the 8th-grade GPA variable from the model.
=+3. Construct and test a path model using the variables Family Background (BYSES), 8th-grade GPA (BYGrads), 10th-grade Self-Esteem (F1Concpt2), 10th-grade Locus of Control(F1Locus2), and 10th-Grade Social Studies Achievement (F1TxHStd). Refer to or redo the analysis. For the sake of consistency,
=+ Can you demonstrate that there are common causes that have been neglected?If the authors included a correlation matrix with their article, see if you can reproduce their results. Draw the estimated model.
=+ Do you think there are any obvious common causes that have not been included in the model?
=+2. Find an article that uses path analysis or explanatory multiple regression on a research topic with which you are familiar and interested. If the authors’ model is not drawn in the article, see if you can draw it from their description. How do the authors justify their causal assumptions or
=+c. Analyze a model like Figure 3, but in which a path is drawn from Ethnicity to Family Background. Now analyze a model in which the path is drawn from Family Background to Ethnicity. Which model is correct? How did you make this decision? What effect, if any, did this change in direction have
=+b. Analyze a model without Parent Involvement. Calculate direct, total, and indirect effects for each variable on GPA. Do the same for the model shown in Figure 3.Compare the tables of direct, indirect, and total effects.
=+a. Make sure you understand what happens when a common cause is omitted versus a simple cause of only one of the variables of interest (Figures 3 through 4). Is Family PATH ANALYSIS: DANGERS AND ASSUMPTIONS Background a common cause or a simple cause of Parent Involvement and GPA? Try deleting
=+1. Conduct each of the parent involvement analyses reported in this chapter, using the NELS data. The variables, as listed in NELS, are: Ethnicity = Ethnic; Family Background =BySES; Previous Achievement = ByTests; Parent Involvement = Par_Inv; and GPA = FfuGrad. Compare your results to mine.
=+ What difference did these different models make in results and interpretation?
=+6. Compare your model and interpretation with others in your class. How many classmates drew the model in the same way you did? How many drew it differently?
=+5. Estimate your model using the variables from NELS (Exercise 4). Calculate the direct effects and disturbances, and put them into your model. Calculate total effects and create a table of direct, indirect, and total effects. Interpret the model; focus on direct, indirect, and total effects.
=+4. Select the variables BYSES, BYGrads, F1Cncpt2, F1Locus2, and F1TxHStd from the NELS data. Check the variables (e.g., descriptive statistics) to make sure you understand the scales of the variables. Also make sure that any values that should be coded as missing values are so coded.
=+3. What is the identification status of your model: just-identified, overidentified, or underidentified? If your model is underidentified, see if you can make it into a just-identified model so that you can estimate it.
=+2. Construct a path model using the variables Family Background, 8th-grade GPA, 10th-grade Self-Esteem, 10th-grade Locus of Control, and 10th-grade Social Studies achievement test scores. How did you make the decisions on which variable affected which? Which of these decisions were the most
=+1. Table 2 shows the means, standard deviations, and correlations among the variables used in this chapter’s example. Reanalyze the five-variable path model. (For users of SPSS, the file “motivate 5 var path.sps” on the Web site (www.ablongman.com/keith1e) shows how to analyze such a
=+3. Do the same regression, adding the variable BYSES to the independent variables (BYParEd is a component of BYSES). Compute collinearity diagnostics for this example. Do you note any problems?
=+Do these cases look okay on these and other variables? What do you propose to do? Discuss your options and decisions in class. (To do this analysis, you may want to create a new variable equal to the case number [e.g., COMPUTE CASENUM=$CASENUM in SPSS]. You can then sort the cases based on each
=+2. Rerun the regression; save standardized and studentized residuals, leverage, Cook’s Distance, and standardized DF Betas. Check out any outliers and unusually influential cases.
=+1. Return to the first regression we did with the NELS data. Regress 10th-grade GPA (FFUGrad) on Parent Education (BYParEd) and Time Spent on Homework Out of School(F1S36A2). Save the unstandardized residuals and predicted values. Use the residuals to test for linearity in the Homework variable
=+Was the article understandable in light of this chapter?
=+ Were the variables of interest centered prior to creating a cross product?
=+ Did the authors use techniques like those described in this chapter?
=+6. Search for an article in your area of interest with the words moderation or moderated regression in the title or abstract. Read the abstract to make sure regression was used. Read the article. Is moderation also referred to as an interaction? Which variables interact? Were they continuous or
=+5. Use a literature research database to find an article in an area of interest to you with the word mediation in either the title or the abstract. Read the abstract to make sure the term mediation refers to statistical mediation (rather than, say, legal mediation). Read the article. Do the
=+4. Does TV viewing have a curvilinear effect on Grades? Spend a few minutes thinking about this question. If you believe TV viewing has such an effect, what do you think will be the shape of the regression line: negative and concave; negative and convex? Use NELS to test this question. Use F1S45A
=+3. Conduct the multiple regression testing the curvilinear effect of Homework on Grades conducted earlier in this chapter. Compare your results to mine. Make sure you are able to correctly center the variables and create the Homework squared term. Graph the curved regression line.
=+test the interaction of TV and Previous Achievement (ByTests). Also control for base year SES (BySES). Is the interaction statistically significant? Graph the interaction (or the lack of an interaction). How do you account for the differences between these findings and those from Exercise 1?
=+2. Conduct a similar analysis using the NELS data. Try using F1S45A as the measure of time spent watching TV and a mean of the 10th-grade test scores (F1TxRStd, F1TxMStd, F1TxSStd, F1TxHStd) as the outcome. Because NELS did not include measures of ability
=+1. If you have not done so already, conduct the multiple regression testing the interaction of TV and Ability on Achievement conducted earlier in this chapter. Compare your results to mine.Make sure you are able to correctly center the variables and create the interaction term.Try the different
=+Analyze the results of the experiment using multiple regression analysis. Test for the presence of an interaction between the pretest and the treatment (type of class). Conduct an ANCOVA and compare the results of this analysis with those of the multiple regression.
=+5. The file “ancova exercise.sav” includes simulated data for the ANCOVA example presented in the chapter (see also the Excel or plain text versions of this file). This was a pretest–posttest two-group design in which 60 students registered for a course in research methodology were
=+4. The file “ATI Data b.sav” (or the Excel or plain text versions of these data) includes another, perhaps more realistic, simulated data set for the attribute–treatment interaction problem illustrated in the chapter. Perform an ATI analysis and interpret the results.
=+3. Is the NELS math test biased against girls? Conduct an analysis of predictive bias using the base year test (ByTxMStd) and Sex, with 10th-grade Math GPA as the outcome (F1S39a).Make sure you convert Sex into a dummy variable and center the Math test score
=+Try conducting the analysis using the uncentered data (and cross product based on uncentered data), as was done in Kranzler et al. (1999). Compare the coefficients and correlations from the two analyses. Would your interpretation be the same? You should find that the intercepts are not
=+2. Use the “Kranzler et al simulated data.sav” (or “Kranzler et al simulated.xls” or “Kranzler.txt”) data set found on the Web site (www.ablongman.com/keith1e). Center the CBM scores and create a Sex by CBM cross product using the centered variable. Conduct an analysis for predictive
=+1. Conduct the first three examples used in this chapter that used the NELS data: the regression of Self-Esteem on Sex and Achievement, the same analysis with the addition of an Achievement by Sex cross product, and the regression of Self-Esteem on Ethnic origin, Achievement, and an Ethnic by
=+7. Determine whether the groups differ without the continuous variable in the equation.Regress the outcome on the categorical variable alone and check for statistical significance. If the categorical variable is statistically significant, this means that the groups have different means, which
=+one dummy variable, we could garner the same information by focusing on the statistical significance of the b associated with the categorical variable (Sex) in the top half of the table of coefficients shown in Figure 14. A difference in intercepts suggests intercept bias, whereas no difference
=+6. Determine whether the intercepts are different for the groups with the continuous variable in the equation. Most generally, you could regress the outcome on the continuous variable, sequentially adding the categorical variable and focusing on the and its statistical significance. In the
=+5. Determine whether the continuous variable is statistically significant across groups(without the cross-product term in the equation). You can do this in two ways. You can regress the outcome on the categorical variable and then add the continuous variable to the regression equation, focusing
=+4. It may be worthwhile to focus on whether the intercepts are also different for the two groups. Given that the interaction was statistically significant, determine whether the associated with the categorical variable (with the continuous variable and the interaction term already in the
=+3. Graph the interaction and conduct separate regressions for each group (e.g., boys and girls) of the outcome variable on the continuous variable. These steps will help you determine the nature of the interaction and the slope bias. Go to step 4.
=+If for the cross product is statistically significant, then the interaction between the categorical and continuous variable is statistically significant; in the context of predictive bias, this suggests the presence of slope bias. If the interaction is statistically significant, go to step 3. If
=+2. Determine whether the interaction is statistically significant. The most general method for doing so is to conduct a simultaneous regression using the categorical and continuous variable and then sequentially add the cross-product (interaction) term(s).
=+1. Determine whether the variance accounted for by the regression including all three terms (the categorical variable, the continuous variable, and the interaction) is statistically significant and meaningful. If not, it makes little sense to proceed. If R2 is meaningful, go to step 2.
=+d. Convert the Family Structure variable into a single criterion scaled variable and conduct the MR using it. Correct the ANOVA table from the MR for the correct degrees of freedom and compare the results with the other analyses of the same data.
=+c. Create effect variables with single-parent families as the group coded –1 on all variables. Regress Substance use on these effect variables and interpret the regression results.
=+b. Create dummy variables contrasting students from two-parent families with those from parent–guardian families and those from single-parent families. Regress Substance Use on these dummy variables. Interpret the overall regression. Use the table of coefficients to conduct post hoc testing.
=+a. Create the Family Structure and Substance Use variables (see note 7). Examine descriptive statistics for each variable, and compute means and standard deviations of Substance Use by Family Structure.
=+2. Conduct the analyses of the effect of Family Structure on students’ Substance Use as outlined in this chapter using the NELS data. This is one of the more complex exercises you will do, because it requires the creation of several new variables. It is also probably one of the more realistic
=+c. Convert the group variable into a single criterion scaled variable and conduct the MR using it. Correct the ANOVA table from the MR for the correct degrees of freedom and compare the results with the other analyses of the same data.
=+b. Convert the group variable into three effect coded variables and analyze the data with MR. Compare the results with the ANOVA and with the dummy coded solution.
=+a. Convert the group variable into g – 1, or three, dummy variables and analyze the data with MR. Use the table of coefficients to conduct the three post hoc procedures. Compare the results with the ANOVA.
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