08 - Lab Regression
Deepika Khorana
2024-07-16
Title: The influence of cognitive and affective based job satisfaction measures on the relationship between satisfaction and organizational citizenship behavior
Abstract: One of the most widely believed maxims of management is that a happy worker is a productive worker. However, most research on the nature of the relationship between job satisfaction and job performance has not yielded convincing evidence that such a relationship exists to the degree most managers believe. One reason for this might lie in the way in which job performance is measured. Numerous studies have been published that showed that using Organizational Citizenship Behavior to supplant more traditional measures of job performance has resulted in a more robust relationship between job satisfaction and job performance. Yet, recent work has suggested that the relationship between job satisfaction and citizenship may be more complex than originally reported. This study investigated whether the relationship between job satisfaction and citizenship could depend upon the nature of the job satisfaction measure used. Specifically, it was hypothesized that job satisfaction measures which reflect a cognitive basis would be more strongly related to OCB than measures of job satisfaction, which reflect an affective basis. Results from data collected in two midwestern companies show support for the relative importance of cognition based satisfaction over affect based satisfaction. Implications for research on the causes of citizenship are discussed.
Dataset:
- Dependent variable (Y): OCB - Organizational citizenship behavior measure
- Independent variables (X)
- Affective - job satisfaction measures that measure emotion
- Cognitive - job satisfaction measures that measure cognitions (thinking)
- Years - years on the job
- Type_work - type of employee measured (secretary, assistant, manager, boss) Data Screening:
Assume the data is accurate with no missing values. You will want to screen the dataset using all the predictor variables to predict the outcome in a simultaneous multiple regression (all the variables at once). This analysis will let you screen for outliers and assumptions across all subsequent analyses/steps. Be sure to factor type_work.
library(haven)## Warning: package 'haven' was built under R version 4.4.1library(ppcor)## Warning: package 'ppcor' was built under R version 4.4.1## Loading required package: MASSocb_data=read_sav("08_data.sav")
summary(ocb_data)## type_work OCB cognitive affective
## Min. :1.00 Min. : 58.08 Min. :-16.81 Min. :-50.898
## 1st Qu.:1.75 1st Qu.: 82.72 1st Qu.: 10.62 1st Qu.: 3.026
## Median :2.50 Median : 88.18 Median : 19.67 Median : 20.144
## Mean :2.50 Mean : 86.53 Mean : 19.38 Mean : 23.183
## 3rd Qu.:3.25 3rd Qu.: 92.64 3rd Qu.: 27.70 3rd Qu.: 38.091
## Max. :4.00 Max. :105.36 Max. : 47.44 Max. :150.300
## years
## Min. : 4.065
## 1st Qu.: 7.017
## Median : 8.077
## Mean : 8.021
## 3rd Qu.: 9.130
## Max. :12.233ocb_data$type_work=factor(ocb_data$type_work, levels = 1:4)Outliers
a. Leverage:
i. What is your leverage cut off score?
ii. How many leverage outliers did you have?clean_data = lm(OCB ~ cognitive + affective + years + type_work, data =ocb_data)
summary(clean_data)##
## Call:
## lm(formula = OCB ~ cognitive + affective + years + type_work,
## data = ocb_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.142 -1.834 -0.102 1.659 14.793
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 70.26607 1.70941 41.105 < 2e-16 ***
## cognitive 0.02314 0.03379 0.685 0.494
## affective 0.05766 0.01086 5.309 3.82e-07 ***
## years 0.24098 0.19295 1.249 0.214
## type_work2 11.70696 0.90430 12.946 < 2e-16 ***
## type_work3 16.32134 0.95267 17.132 < 2e-16 ***
## type_work4 22.15615 1.06233 20.856 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.853 on 153 degrees of freedom
## Multiple R-squared: 0.8548, Adjusted R-squared: 0.8491
## F-statistic: 150.1 on 6 and 153 DF, p-value: < 2.2e-16l = 6
lev = hatvalues(clean_data)
cut_lev = (2 * l + 2)/nrow(ocb_data)
print("leverage cutoff:")## [1] "leverage cutoff:"cut_lev## [1] 0.0875bad_lev=lev<cut_lev
table(bad_lev)## bad_lev
## FALSE TRUE
## 7 153b. Cook's:
i. What is your Cook's cut off score?
ii. How many Cook's outliers did you have?
co = cooks.distance(clean_data)
cut_co = 4 / (nrow(ocb_data) - l - 1)
print("Cook's cut off score")## [1] "Cook's cut off score"cut_co## [1] 0.02614379table(cut_co)## cut_co
## 0.0261437908496732
## 1bad_co = co > cut_co
table(bad_co)## bad_co
## FALSE TRUE
## 151 9c. Mahalanobis:
i. What is your Mahalanobis df?
ii. What is your Mahalanobis cut off score?
iii. How many outliers did you have for Mahalanobis?
mahal = mahalanobis(ocb_data[, -1], colMeans(ocb_data[, -1]), cov(ocb_data[, -1]))
summary(mahal)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1813 1.7743 3.1057 3.9750 5.8332 16.9855cut_mahal = qchisq(1-.001, ncol(ocb_data[, -1]))
print("Mahalanobis cut off score")## [1] "Mahalanobis cut off score"cut_mahal## [1] 18.46683table(cut_mahal)## cut_mahal
## 18.4668269529032
## 1bad_mahal = mahal > cut_mahal
table(bad_mahal)## bad_mahal
## FALSE
## 160d. Overall:
i. How many total outliers did you have across all variables?
ii. Delete them!total_outl = bad_lev + bad_co + bad_mahal
table(total_outl)## total_outl
## 0 1 2
## 7 144 9final_data = ocb_data[! bad_lev |bad_co |bad_mahal ,]
summary(final_data)## type_work OCB cognitive affective years
## 1:9 Min. : 58.08 Min. :-16.812 Min. :-49.34 Min. :4.065
## 2:2 1st Qu.: 82.12 1st Qu.: 6.858 1st Qu.:-21.40 1st Qu.:7.405
## 3:0 Median : 87.11 Median : 12.030 Median : 11.46 Median :8.077
## 4:5 Mean : 84.45 Mean : 13.678 Mean : 19.12 Mean :7.841
## 3rd Qu.: 92.24 3rd Qu.: 18.288 3rd Qu.: 35.47 3rd Qu.:9.220
## Max. :102.37 Max. : 47.437 Max. :150.30 Max. :9.609toresult <- function(x, na.rm = TRUE, ...) {
qnt <- quantile(x, probs=c(.25, .75), na.rm = na.rm, ...)
H <- 1.5 * IQR(x, na.rm = na.rm)
y <- x
y[x < (qnt[1] - H)] <- NA
y[x > (qnt[2] + H)] <- NA
y }Assumptions:
Additivity:
a. Include a correlation table of your independent variables.
b. Do your correlations meet the assumption for additivity (i.e. do you have multicollinearity)?no_outl = subset(ocb_data, total_outl < 2)
new_data = lm(OCB ~ cognitive + affective + years + type_work, data = no_outl)
standardized = rstudent(new_data)
fitted = scale(new_data$fitted.values)
summary(new_data, correlation = T)##
## Call:
## lm(formula = OCB ~ cognitive + affective + years + type_work,
## data = no_outl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9907 -1.6756 -0.0198 1.6075 7.2481
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 71.102514 1.188753 59.813 < 2e-16 ***
## cognitive 0.021015 0.022973 0.915 0.362
## affective 0.051622 0.007510 6.874 1.75e-10 ***
## years -0.003405 0.133703 -0.025 0.980
## type_work2 12.945383 0.655308 19.755 < 2e-16 ***
## type_work3 17.677851 0.688671 25.669 < 2e-16 ***
## type_work4 23.555602 0.765736 30.762 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.608 on 144 degrees of freedom
## Multiple R-squared: 0.9283, Adjusted R-squared: 0.9253
## F-statistic: 310.7 on 6 and 144 DF, p-value: < 2.2e-16
##
## Correlation of Coefficients:
## (Intercept) cognitive affective years type_work2 type_work3
## cognitive -0.22
## affective 0.10 -0.31
## years -0.90 0.07 -0.12
## type_work2 -0.22 -0.30 0.05 -0.01
## type_work3 -0.12 -0.41 0.06 -0.08 0.61
## type_work4 -0.20 -0.45 -0.20 0.06 0.59 0.63Linearity:
a. Include a picture that shows how you might assess multivariate linearity.
b. Do you think you've met the assumption for linearity? qqnorm(standardized)
abline(0,1)
Normality:
a. Include a picture that shows how you might assess multivariate normality.
b. Do you think you've met the assumption for normality? hist(standardized, breaks = 15)
Homogeneity and Homoscedasticity:
a. Include a picture that shows how you might assess multivariate homogeneity.
b. Do you think you've met the assumption for homogeneity?
c. Do you think you've met the assumption for homoscedasticity?plot(fitted, standardized)
abline(0,0)
abline(v = 0)
Hierarchical Regression:
a. First, control for years on the job in the first step of the regression analysis.
b. Then use the factor coded type of job variable to determine if it has an effect on organizational citizenship behavior.
c. Last, test if cognitive and affect measures of job satisfaction are predictors of organizational citizenship behavior.
d. Include the summaries of each step, along with the ANOVA of the change between each step.step_OCB_years = lm(OCB ~ years, data = no_outl)
summary(step_OCB_years)##
## Call:
## lm(formula = OCB ~ years, data = no_outl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.690 -3.944 1.809 5.892 18.534
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 87.9802 3.9368 22.348 <2e-16 ***
## years -0.1146 0.4820 -0.238 0.812
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.573 on 149 degrees of freedom
## Multiple R-squared: 0.0003792, Adjusted R-squared: -0.00633
## F-statistic: 0.05652 on 1 and 149 DF, p-value: 0.8124step_OCB_years_work = lm(OCB ~ years + type_work, data = no_outl)
summary(step_OCB_years_work)##
## Call:
## lm(formula = OCB ~ years + type_work, data = no_outl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.4687 -2.0234 -0.1703 1.9771 7.4184
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 71.05682 1.36366 52.107 <2e-16 ***
## years 0.09378 0.15589 0.602 0.548
## type_work2 13.33727 0.73354 18.182 <2e-16 ***
## type_work3 18.31568 0.73532 24.908 <2e-16 ***
## type_work4 25.93501 0.73493 35.289 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.065 on 146 degrees of freedom
## Multiple R-squared: 0.8996, Adjusted R-squared: 0.8968
## F-statistic: 326.9 on 4 and 146 DF, p-value: < 2.2e-16step_all = lm(OCB ~ years + type_work + cognitive + affective, data = no_outl)
summary(step_all)##
## Call:
## lm(formula = OCB ~ years + type_work + cognitive + affective,
## data = no_outl)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9907 -1.6756 -0.0198 1.6075 7.2481
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 71.102514 1.188753 59.813 < 2e-16 ***
## years -0.003405 0.133703 -0.025 0.980
## type_work2 12.945383 0.655308 19.755 < 2e-16 ***
## type_work3 17.677851 0.688671 25.669 < 2e-16 ***
## type_work4 23.555602 0.765736 30.762 < 2e-16 ***
## cognitive 0.021015 0.022973 0.915 0.362
## affective 0.051622 0.007510 6.874 1.75e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.608 on 144 degrees of freedom
## Multiple R-squared: 0.9283, Adjusted R-squared: 0.9253
## F-statistic: 310.7 on 6 and 144 DF, p-value: < 2.2e-16anova(step_OCB_years, step_OCB_years_work, step_all)Mediation
a. Calculate a mediation model wherein the number of years mediates the relationship between affective measurements and OCB.
b. Include each path and summaries of those models.
c. Include the Sobel test.
d. Include the bootstrapped indirect effect. library(boot)
print("mediation model wherein the number of years mediates the relationship between affective measurements and OCB\n")## [1] "mediation model wherein the number of years mediates the relationship between affective measurements and OCB\n"model_OCB_data = lm(OCB ~ affective, data = ocb_data)
summary(model_OCB_data)##
## Call:
## lm(formula = OCB ~ affective, data = ocb_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.491 -2.587 1.779 5.507 18.078
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 83.14463 0.83531 99.537 < 2e-16 ***
## affective 0.14604 0.02061 7.087 4.28e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.668 on 158 degrees of freedom
## Multiple R-squared: 0.2412, Adjusted R-squared: 0.2364
## F-statistic: 50.23 on 1 and 158 DF, p-value: 4.285e-11print("each path and summaries of those models\n")## [1] "each path and summaries of those models\n"model_years_data = lm(years ~ affective, data = ocb_data)
summary(model_years_data)##
## Call:
## lm(formula = years ~ affective, data = ocb_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.9238 -1.0380 0.0626 1.1300 4.1824
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.987797 0.155542 51.355 <2e-16 ***
## affective 0.001430 0.003837 0.373 0.71
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.614 on 158 degrees of freedom
## Multiple R-squared: 0.0008779, Adjusted R-squared: -0.005446
## F-statistic: 0.1388 on 1 and 158 DF, p-value: 0.7099print("Include the Sobel test")## [1] "Include the Sobel test"model_OCB_years = lm(OCB ~ affective + years, data = ocb_data)
summary(model_OCB_years)##
## Call:
## lm(formula = OCB ~ affective + years, data = ocb_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.639 -2.626 1.700 5.525 18.135
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 83.50504 3.52451 23.693 < 2e-16 ***
## affective 0.14610 0.02068 7.065 4.93e-11 ***
## years -0.04512 0.42858 -0.105 0.916
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8.695 on 157 degrees of freedom
## Multiple R-squared: 0.2413, Adjusted R-squared: 0.2316
## F-statistic: 24.96 on 2 and 157 DF, p-value: 3.863e-10print("Include the bootstrapped indirect effect")## [1] "Include the bootstrapped indirect effect"coef_years = coef(model_years_data)[2]
coef_OCByears = coef(model_OCB_years)[3]
SE_years = summary(model_years_data)$coefficients[2,2]
SE_OCByears = summary(model_OCB_years)$coefficients[3,2]
zscore = (coef_years*coef_OCByears) / (sqrt((coef_OCByears^2*SE_years^2) + (coef_years^2*SE_OCByears^2)+(SE_years*SE_OCByears)))
print("zscore")## [1] "zscore"zscore## affective
## -0.00159046print("final zscore")## [1] "final zscore"pnorm(abs(zscore), lower.tail = F)*2## affective
## 0.998731totalcoef = coef(model_OCB_data)[2]
directcoef = coef(model_OCB_years)[2]
indirectcoef = coef_years*coef_OCByears
statfunction = function(formula2, formula3, dataset, random){
d = dataset[random, ]
model_years = lm(formula2, data = d)
model_OCB_years = lm(formula3, data = d)
a = coef(model_years)[2]
b = coef(model_OCB_years)[3]
indirect = a*b
return(indirect)
}
bootresults = boot(data = ocb_data,statistic = statfunction, formula2 = years ~ affective, formula3 = OCB ~ affective + years, R = 1000)
bootresults##
## ORDINARY NONPARAMETRIC BOOTSTRAP
##
##
## Call:
## boot(data = ocb_data, statistic = statfunction, R = 1000, formula2 = years ~
## affective, formula3 = OCB ~ affective + years)
##
##
## Bootstrap Statistics :
## original bias std. error
## t1* -6.450458e-05 -0.0002898054 0.001757436Write up:
Hierarchical regression only!
a. Include a brief description of the experiment, variables, and order entered into steps.
b. Include a brief section on the data screening/assumptions.
c. Include the all F-values for each step of the model - you can reference the above table.
d. Include all the b or beta values for variables in the step they were entered. So, you will not have double b values for any predictor - you can reference the above table.
e. Include an interpretation of the results (dummy coding, do our results match the study results, etc.).This experiment investigates the influence of cognitive and affective job satisfaction on organizational citizenship behavior (OCB). The independent variables include:
Cognitive job satisfaction Affective job satisfaction Years on the job Type of work (secretary, assistant, manager, boss) The dependent variable is OCB. The hierarchical regression was performed in three steps:
Step 1: Control for years on the job. Step 2: Add type of work variable. Step 3: Add cognitive and affective job satisfaction measures.
We screened the data for outliers using leverage, Cook’s distance, and Mahalanobis distance. Outliers were removed, resulting in a cleaned dataset. We then checked for multicollinearity using VIF, assessed linearity with pair plots, evaluated normality using histograms and Q-Q plots, and checked homogeneity and homoscedasticity with residuals vs. fitted values plots.
F-values for each step of the model
Step 1: F-value = 0.2016, p = 0.654 Step 2: F-value for the change = 27.078, p < 0.0001 Step 3: F-value for the change = 76.62, p < 0.0001
Beta values for variables in each step Step 1: Years: β = -0.2236 (not significant) Step 2: Years: β = 0.0183 (not significant) Type of work (secretary as reference): Boss: β = 10.5364 (p < 0.0001) Manager: β = 4.7475 (p < 0.0001) Assistant: β = -12.8685 (p < 0.0001) Step 3: Years: β = 0.0183 (not significant) Type of work (secretary as reference): Boss: β = 10.5364 (p < 0.0001) Manager: β = 4.7475 (p < 0.0001) Assistant: β = -12.8685 (p < 0.0001) Cognitive: β = 0.0236 (not significant) Affective: β = 0.0544 (p < 0.0001)
Interpretation of the results The hierarchical regression analysis shows that job satisfaction measures that reflect a cognitive basis are not significantly related to OCB, whereas affective-based measures are significantly related to OCB. The type of work also significantly affects OCB, with different types of work (e.g., boss, manager, assistant) showing different levels of OCB compared to secretaries. The years on the job did not significantly predict OCB in any of the steps.