Assignment and Exercises Write a 1,050- to 1,400-word paper that includes the following: · Assess the major concepts and components for hierarchical linear regression and multilevel modeling. See...

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Assignment and Exercises Write a 1,050- to 1,400-word paper that includes the following: · Assess the major concepts and components for hierarchical linear regression and multilevel modeling. See Exercise 8B – pages 2 through 20 · Replicate the major tables for hierarchical regression and after each of the primary tables explain (from your own understanding) the primary results that are shown in certain columns that lead to the interpretation of test results and the decisions to reject or failure to reject (i.e., retain or accept) the null hypotheses. Evaluate the strengths and weaknesses or limitations of the model. See Exercise 9B – pages 21 – 38 · Replicate the major tables for multilevel modeling and after each of the primary tables explain (from your own understanding) the primary results that are shown in certain table columns that lead to the interpretation of the test results and the decision to reject or failure to reject (i.e., retain or accept) the null hypotheses. Evaluate the strengths and weaknesses or limitations of the model. · Draw conclusions about how hierarchical analysis is related to the multilevel analysis and the interaction effects of variables in both the models. Exercise 8B Multiple Regression: Beyond Statistical Regression Using IBM SPSS 8B.1 Hierarchical Linear Regression We use the example of hierarchical linear regression that was described in Section 8A.2.2. In that example, we were interested in predicting the level of awareness of cultural barriers believed to be faced by their clientele as reported by mental health practitioners. The key predictors we used were a subscale assessing institutional discrimination, a subscale assessing ethnic identity exploration, and collectivism orientation. Control variables were social desirability and two sample characteristics variables dealing with the length of time spent as a provider in mental health and whether or not the practitioners had received specialized training in multicultural counseling. The data set we use here is Victoria. 8B.1.1 Hierarchical Regression Analysis Setup Selecting the path Analyze  Regression  Linear from the main menu brings us to the Linear Regression main dialog window displayed in Figure 8b.1. From the variables list panel, we click over CBMCSACB (California Brief Multicultural Competence Scale Awareness of Cultural Barriers subscale) to the Dependent panel and MCSDS (Marlowe–Crowne Social Desirability scale) to the Independent(s) panel. This will be the first “block” or “set” of variables in the hierarchical analysis. The Method drop-down menu will be left at its default setting of Enter, which specifies that the variables we have in the panel will be entered simultaneously in that block (with only one variable, it does not matter anyway). Click the Next pushbutton to reset the window so that the second block of variables can be specified. Figure 8b.1   The First Block of the Hierarchical Analysis Will Enter Social Desirability Into the Model With the main dialog window reset and the Independent(s) panel now empty, place YearMenHlth (years of mental health experience) and MCWorkshp (yes coded as 1 and no coded as 0 for having participated in a multicultural workshop for mental health practitioners) into the Independent(s) panel (see Figure 8b.2). This will be the second block or set of variables in the hierarchical analysis. The Method drop-down menu will be left at its default setting of Enter, which specifies that the variables we have in the panel will be entered simultaneously in that block (although we have not done so, we could have specified one of the step methods). Click the Next pushbutton to reset the window so that the third and final block of variables can be specified. Once again we are presented with an empty Independent(s) panel into which we now place COBRASID (Color-Blind Racial Attitudes Scale Institutional Discrimination sub-scale), MEIMEIE (Multigroup Ethnic Identity Measure Ethnic Identity Exploration sub-scale), and INDCOLC (Individual/Collectivism scale Collectivism subscale) as shown in Figure 8b.3. The Method drop-down menu will be left at its default setting of Enter, which specifies that these variables will be entered simultaneously. Set up the Statistics window as we have done in the previous chapters (see Figure 8b.4), click Continue to return to the main dialog window, and select OK to perform the analysis. Figure 8b.2   The Second Block of the Hierarchical Analysis Will Enter the Two Experience Variables Into the Model Figure 8b.3   The Third and Final Block of the Hierarchical Analysis Will Enter Institutional Discrimination, Ethnic Identity Exploration, and Collectivism Into the Model Figure 8b.4   The Statistics Window 8B.1.2 Hierarchical Regression Analysis Output The correlation matrix of the variables is shown in Figure 8b.5. As we have already seen, the dependent variable is placed in the first row and first column. The correlations of the other predictors are quite modest, with the highest being associated with institutional discrimination. As can be seen, awareness of cultural barriers is not significantly (p = .176) correlated with social desirability (r = −.049), and thus, its effect as a covariate is likely to be minimal. Figure 8b.6 presents the results of the significance testing of the models. This output and the output that follows is structured akin to the way in which the output from a step analysis is structured. Here, each model corresponds to each block of variables that we entered in succession. The results of the first block confirm what we saw from the correlation matrix: Social desirability did not significantly increase our predictive ability. The second block, composed of the experience variables, and the third block, composed of our predictors of interest, each were statistically significant, that is, a statistically significant amount of prediction was obtained for each of these blocks. The main results are contained in the two tables shown in Figure 8b.7. We can see in the Model Summary that the R2 value went from .002 to .030 to .276 over the three hierarchical blocks of variables, with the R2 change being statistically significant for the second and third blocks. Figure 8b.5   Correlations of the Variables Figure 8b.6   Statistical Significance of the Models Figure 8b.7   The Main Regression Results The Coefficients table tracks the changes in the model as variables were entered. After the second block, not having participated in a multicultural workshop predicts greater awareness when social desirability and years of experience are statistically controlled, which may be of some theoretical and practical interest to the researchers. But the dynamics evolve. After the third and final block where only the primary three variables—institutional discrimination, ethnic identity exploration, and collectivism—emerge as the statistically significant predictors in the model controlling for the other variables. The workshop variable is no longer statistically significant at the .05 level and social desirability is very close to statistical significance, and these trends might provide the impetus to further research. 8B.1.3 Reporting Hierarchical Multiple Regression Results A three-stage hierarchical linear regression analysis was used to predict the level of awareness of cultural barriers believed to be faced by their clientele as reported by mental health practitioners. In the first block, social desirability was entered as a covariate; in the second block, the number of years spent as a provider in mental health and whether or not the practitioners had received specialized training in multicultural counseling were simultaneously entered; in the third block, institutional discrimination, ethnic identity exploration, and collectivism orientation were entered simultaneously as the primary variables of interest. The correlations of the variables are shown in Table 8b.1. As can be seen, the awareness of barriers variable correlated most strongly with institutional discrimination and ethnic identity exploration. Results of the hierarchical regression analysis are shown in Table 8b.2. Social desirability, entered on the first block, was not a significant covariate, F(1, 366) = 0.870, p = .352. When the two experience variables were added on the second block, the prediction model was statistically significant, F(3, 364) = 3.804, p = .010, R2 = .030, Adjusted R2 = .022. In the second block, not having participated in a multicultural workshop modestly predicted greater awareness of cultural barriers. For the final block, the model increased substantially in its predictive power, F(6, 361) = 22.902, p < .001, r2 = .276, adjusted r2 = .264. the strongest predictor of the set was institutional discrimination followed by ethnic identity exploration and a collectivism orientation. generally, with all other variables in the analysis statistically controlled, those whose views on discrimination have been negatively driven by the culture, who are more inclined to explore their ethnic identity, and who have more of a collectivist orientation reported greater awareness of their clientele’s cultural barriers. based on the structure coefficients, it appears that the latent variable described by the model is best indicated by institutional discrimination. 8b.2 polynomial regression 8b.2.1 the example for polynomial regression our example for polynomial regression is based on a set of real test data that have been substantially modified and simplified for the present purposes. it has been known since the middle of the past century (lord, 1953; mollenkopf, 1949; thorndike, 1951) that the value of the standard error of measurement (a statistic that estimates measurement error and which serves as a basis to establish confidence intervals—margins of error—around scores) varies across the range of test scores; when focusing on any single test score, it is known as the conditional standard error of measurement. table 8b.1   correlations of the variables in the analysis (n = 368) based on the analysis of some test data collected from an entry-level state selection exam that one of the authors and a team of his graduate students developed for a large job classification, it was possible to estimate the standard error of measurement over a range of test scores. the pattern of the data is shown in the scatterplot of figure 8b.8. the data are contained in the file named polynomial. in this modified and simplified version of the data set, a standard error of measurement was estimated for test scores ranging from 15 to 45 items correct. as can be seen from figure 8b.8, there appear to be two minimum/maximum locations in the function, a maximum between the test scores of 20 and 30 and a minimum just over a test score of 40. the presence of two such minimum/maximum locations suggests that a cubic (x3) function would represent the relationship between test score and the standard error. for the purposes of this example, assume that we wished to generate the model that best represented the relationship between the estimated standard error of measurement and test score. given the observed pattern of the scatterplot, we might hypothesize that an important aspect of the function (assessed by r2) was cubic but that a significant quadratic aspect of the function might materialize [because that portion of the function to the left of a test score of 40 appears to give a strong impression of a quadratic (x2) relationship]. furthermore, because the data generally “angle downward” from left to right (a negatively sloped straight line), some of the variance would likely be explained by a linear component. table 8b.2   hierarchical regression results (n = 368) 8b.2.2 polynomial regression setup to examine the polynomial relationship between the estimated standard error of measurement and test score, the first step is to build the quadratic and cubic variables to use as additional predictors. we thus computed the squared (quadratic) and cubic values of test_score, the syntax for which is shown in figure 8b.9. in the syntax, the double asterisks indicate “exponent.” these variables are already contained in the data file. figure 8b.8   a scatterplot .001, r2 =".276," adjusted r2 =".264." the="" strongest="" predictor="" of="" the="" set="" was="" institutional="" discrimination="" followed="" by="" ethnic="" identity="" exploration="" and="" a="" collectivism="" orientation.="" generally,="" with="" all="" other="" variables="" in="" the="" analysis="" statistically="" controlled,="" those="" whose="" views="" on="" discrimination="" have="" been="" negatively="" driven="" by="" the="" culture,="" who="" are="" more="" inclined="" to="" explore="" their="" ethnic="" identity,="" and="" who="" have="" more="" of="" a="" collectivist="" orientation="" reported="" greater="" awareness="" of="" their="" clientele’s="" cultural="" barriers.="" based="" on="" the="" structure="" coefficients,="" it="" appears="" that="" the="" latent="" variable="" described="" by="" the="" model="" is="" best="" indicated="" by="" institutional="" discrimination.="" 8b.2="" polynomial="" regression="" 8b.2.1="" the="" example="" for="" polynomial="" regression="" our="" example="" for="" polynomial="" regression="" is="" based="" on="" a="" set="" of="" real="" test="" data="" that="" have="" been="" substantially="" modified="" and="" simplified="" for="" the="" present="" purposes.="" it="" has="" been="" known="" since="" the="" middle="" of="" the="" past="" century="" (lord,="" 1953;="" mollenkopf,="" 1949;="" thorndike,="" 1951)="" that="" the="" value="" of="" the="" standard="" error="" of="" measurement="" (a="" statistic="" that="" estimates="" measurement="" error="" and="" which="" serves="" as="" a="" basis="" to="" establish="" confidence="" intervals—margins="" of="" error—around="" scores)="" varies="" across="" the="" range="" of="" test="" scores;="" when="" focusing="" on="" any="" single="" test="" score,="" it="" is="" known="" as="" the="" conditional="" standard="" error="" of="" measurement.="" table="" 8b.1   correlations="" of="" the="" variables="" in="" the="" analysis="" (n ="368)" based="" on="" the="" analysis="" of="" some="" test="" data="" collected="" from="" an="" entry-level="" state="" selection="" exam="" that="" one="" of="" the="" authors="" and="" a="" team="" of="" his="" graduate="" students="" developed="" for="" a="" large="" job="" classification,="" it="" was="" possible="" to="" estimate="" the="" standard="" error="" of="" measurement="" over="" a="" range="" of="" test="" scores.="" the="" pattern="" of="" the="" data="" is="" shown="" in="" the="" scatterplot="" of figure="" 8b.8.="" the="" data="" are="" contained="" in="" the="" file="" named polynomial.="" in="" this="" modified="" and="" simplified="" version="" of="" the="" data="" set,="" a="" standard="" error="" of="" measurement="" was="" estimated="" for="" test="" scores="" ranging="" from="" 15="" to="" 45="" items="" correct.="" as="" can="" be="" seen="" from figure="" 8b.8,="" there="" appear="" to="" be="" two="" minimum/maximum="" locations="" in="" the="" function,="" a="" maximum="" between="" the="" test="" scores="" of="" 20="" and="" 30="" and="" a="" minimum="" just="" over="" a="" test="" score="" of="" 40.="" the="" presence="" of="" two="" such="" minimum/maximum="" locations="" suggests="" that="" a="" cubic="" (x3)="" function="" would="" represent="" the="" relationship="" between="" test="" score="" and="" the="" standard="" error.="" for="" the="" purposes="" of="" this="" example,="" assume="" that="" we="" wished="" to="" generate="" the="" model="" that="" best="" represented="" the="" relationship="" between="" the="" estimated="" standard="" error="" of="" measurement="" and="" test="" score.="" given="" the="" observed="" pattern="" of="" the="" scatterplot,="" we="" might="" hypothesize="" that="" an="" important="" aspect="" of="" the="" function="" (assessed="" by r2)="" was="" cubic="" but="" that="" a="" significant="" quadratic="" aspect="" of="" the="" function="" might="" materialize="" [because="" that="" portion="" of="" the="" function="" to="" the="" left="" of="" a="" test="" score="" of="" 40="" appears="" to="" give="" a="" strong="" impression="" of="" a="" quadratic="" (x2)="" relationship].="" furthermore,="" because="" the="" data="" generally="" “angle="" downward”="" from="" left="" to="" right="" (a="" negatively="" sloped="" straight="" line),="" some="" of="" the="" variance="" would="" likely="" be="" explained="" by="" a="" linear="" component.="" table="" 8b.2   hierarchical="" regression="" results="" (n ="368)" 8b.2.2="" polynomial="" regression="" setup="" to="" examine="" the="" polynomial="" relationship="" between="" the="" estimated="" standard="" error="" of="" measurement="" and="" test="" score,="" the="" first="" step="" is="" to="" build="" the="" quadratic="" and="" cubic="" variables="" to="" use="" as="" additional="" predictors.="" we="" thus="" computed="" the="" squared="" (quadratic)="" and="" cubic="" values="" of test_score,="" the="" syntax="" for="" which="" is="" shown="" in figure="" 8b.9.="" in="" the="" syntax,="" the="" double="" asterisks="" indicate="" “exponent.”="" these="" variables="" are="" already="" contained="" in="" the="" data="" file.="" figure="" 8b.8   a="">
Answered Same DayAug 18, 2021

Answer To: Assignment and Exercises Write a 1,050- to 1,400-word paper that includes the following: · Assess...

Mohd answered on Aug 22 2021
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Multiple Regression: Beyond Statistical Regression Using IBM SPSS
first block, social desirability entered as a covariate; in the second block, the number of years experience mental health and whether or not the pra
ctitioners had received specialized training in multicultural counseling were simultaneously entered; in the third block, institutional discrimination, ethnic identity exploration, and collectivism orientation were entered simultaneously.
First block, was not a significant covariate p = .352. Two experience variables were added on the second block, the prediction model was statistically significant, F(3, 364) = 3.804, p = .010, R2 = .030,AdjustedR2=.022.
For the final block, the model increased substantially in its predictive power with p < .001, R2 = .276, Adjusted R2 = .264.
Polynomial Regression
All three models were statistically significant:
· The linear component, F(1, 29) = 13.979, p < .001, R2 = .592, Adjusted R2 = .578.
· The combined linear and quadratic components, F(2, 28) = 9.134, p < .001, R2 = .774, Adjusted R2 = .758.
· The combined linear, quadratic, and cubic components, F(3, 27) = 7.824, p < .001, R2 = .995, Adjusted R2 = .994.
It seems that a cubic function containing both the linear and quadratic terms almost fully responsible for the shape of the function.
Dummy and Effect Coding
Effects Coded Regression Output
The only mean that is useful is the one for the evaluation ratings with a value of 5.96
The model is statistically significant; with 2 and 21 degrees of freedom, the F ratio of 37.848 exceeds our alpha level of .05 (p < .001). R2 =0.783.
Group Means and Regression Coefficients
Interaction Effects of Quantitative Variables in Regression
Positive affect significantly predicted the variable of self-control, F(1, 420) = 81.045, p < .001, R2 = .162, Adjusted R2 = .160; its b coefficient was .071 (SE = 0.008) and its beta coefficient was .402 F(1, 420) = 186.452, p < .001, R2 = .307 Adjusted R2 = .306;

In the mediated both positive affect and self-esteem significantly predicted the outcome variable of self-control, F(2, 419) = 67.338, p < .001, R2 = .243, Adjusted R2...
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