I am conducting a research on the effect of excellence on job satisfaction. One type of questionnaire was addressed to employees while the other was addressed to customers. The number of responses collected from employees is more than from customers.
In an earlier post, I stated that “If you don't have values associated with an individual for every single variable you include in your regression model, standard computer programs will drop all data for the individual out of the calculations.” Since software for standard (ordinary least squares or OLS) regression may not give you an explicit warning message that this has happened, I’ll use this post to describe and demonstrate what that looks like to the subject matter specialist using statistics.
As part of your regression analysis you will get a table of numbers that includes an overall p-value and individual p-values for each variable you included in your regression model. That table will also include a column of numbers labeled df or degrees of freedom. If you add up all the degrees of freedom on the table, the sum will be one (1) less than the total number of individuals (subjects, records, samples, organizations, …) used in calculating the regression (or other OLS ANOVA table). The unreported degree of freedom was used to calculate the overall average for the “y” variable. A simulation follows my signature with data vaguely similar to those discussed in this thread. The software used is R.
Again, I wish you much success in your research.
Chuck
Note that the following is best viewed by copying and pasting into something allowing the use of Courier or some other non-proportional font:
> # Demonstrated Effect of Missing Values in OLS Regression
> # Let es = Employee's Satisfaction
> # ee = Employee's Measure of Excellence
> # ce = Customer's Measure of Excellence
> # cf = Customer's Measure of Friendliness
>
> # Data are generated with measures of 1 to 5 equally
> # likely for all for variables.
> # Let satisfy1 = Dataset for all satisfaction measures
> # satisfy2 = satisfy1 with one measurement missing for cf
> es ee ce cf satisfy1 satisfy2 satisfy2[1,4]
> # Display the datasets
> satisfy1
es ee ce cf
1 4 3 3 2
2 1 4 2 3
3 3 5 3 1
4 1 4 3 5
5 4 4 2 4
6 3 1 1 3
> satisfy2
es ee ce cf
1 4 3 3 NA
2 1 4 2 3
3 3 5 3 1
4 1 4 3 5
5 4 4 2 4
6 3 1 1 3
>
> # OLS Model 1: Regression with Ordinary Least Squares (OLS)
> olsmod1 anova(olsmod1)
Analysis of Variance Table
Response: es
Df Sum Sq Mean Sq F value Pr(>F)
ee 1 0.4211 0.4211 0.1190 0.7630
ce 1 0.1570 0.1570 0.0444 0.8527
cf 1 1.6774 1.6774 0.4740 0.5623
Residuals 2 7.0779 3.5390
> # The sume of the Df (degrees of freedom) is the number of employees minus 1
>
> # OLS Model 2: OLS with a single missing covariate value
> olsmod2 anova(olsmod2)
Analysis of Variance Table
Response: es
Df Sum Sq Mean Sq F value Pr(>F)
ee 1 0.1565 0.1565 0.0280 0.8945
ce 1 0.9810 0.9810 0.1753 0.7476
cf 1 0.4656 0.4656 0.0832 0.8212
Residuals 1 5.5969 5.5969
> # Sum the Df. With a single missing covariate,
> # an entire employee record is removed from OLS calculations.
Mahfuz,
Regression will only work on the intersection of these two data sets (i.e., where you have a value for both). An alternative is to consider replacing missing values (e.g. with means), but this often creates many problems, including reducing variances artificially.
Yes, it can be used and it works e.g. if you would like to regress economic sectors against GDP, and you have data of 14 year for economic sector and 13 years for GDP, the regression will work. but you have to mention 2013 GDP is not included because, until now it is not announced. At the end, yes, you can use it but you have to justify.
Sorry, my first answer was correct but generic. Regarding to your research, yes, you can use regression, even if the customers responses collected are more than the employees responses. I think you have main hypothesis (effect of excellence on job satisfaction). And you have two sub-hypotheses: effect of excellence on job satisfaction (customer perception), effect of excellence on job satisfaction (employees perception). If you would like to evaluate effect of one variable on one variable, it is better to use simple linear regression. If you would like to evaluate more than one independent variable on one independent variable you have to use linear multiple regression. If more than two independent variables on one dependent variable, first you use multiple regressions, then step-wise regression.
Are you trying to research the effect of employee excellence or organizational excellence? If you are researching the effect of employee excellence, is there more than one customer response per employee?
Thanks.
Chuck
I'm not sure regression is the way to go, but let's stick with that for a moment:
Since you have more employee answers than customer answers, try this strategy: let the customer opinions be Y and the employee opinions be X (independent side). Then, run a mixed model regression with employee opinions defined as random.
That said, I have to wonder if you perhaps want to do a correlation analysis, rather than regression. The two methods are related mathematically, but are intended to address different questions. You would still want to use a mixed modeling methodology, whereby eblups are used in the modeling.
In any case, don't replace missing data with averages, particularly if you suspect your missing data are not missing at random..
Dear Mary,
Thank you for your valuable reply, and I think that I will try to do correlation analysis rather than regression.
Sorry gentleman, correlation does not show the effect of excellence on job satisfaction.
To me, how much of the data you can use somewhat depends on whether you are estimating a relationship between excellence of individuals versus individual job satisfaction or between the excellence of an organization versus job satisfaction at that organization. In either case, I am assuming that the measure for satisfaction is expressed as a single number and that you are using multiple regression to predict that value based on a number of survey responses.
If individuals are your primary unity of analysis then the problem presented by Mark Clatworthy applies. If you don't have values associated with an individual for every single variable you include in your regression model, standard computer programs will drop all data for the individual out of the calculations. This isn't something to debate with editors, it has to do with the underlying mathematics. There are a variety of unsatisfactory methods (including modern methods for sparse matrices) to replace the missing values or you can simply leave them missing. No matter how you handle the missing data, your explanation will probably inspire some exchange with your editors at publication.
If organizations are your primary unity of analysis and your survey was conducted at more than a few organizations, you could use some kind of summary statistic (like an arithmetic average) for each organizations response to each variable and possibly avoid the issue of missing values. That still leaves an issue about how you would weight variable responses that came from different numbers of respondents but the journal editors need something to talk about anyway.
I wish you much success with your research.
Chuck
Hey. What you generally describe is a dyadic design (presumed you can match employees and customers). Therefore, ordinary regression analysis will not work. However, you can use multilevel modeling (which can be described as multiple, multiple regressions). This procedure accounts for the dyadic design; e.g., for the fact that one employee serves different customers.
Here is a link, which could be helpful:
http://davidakenny.net/dyad.htm
A common software to estimate multilevel models is HLM http://www.ssicentral.com/hlm/
Best
Tobias
The challenge (if I understand your design and research question correctly) seems to be to connect employees and customers. I guess you can connect multiple customers to respective employees or (if you have data from multiple firms or sites) connect all cusomers and all employees at the same site. In any case you either need to aggregate responses from customers (assuming customer responses converge per employee or per firm) or use multilevel models as suggested above.
And I see another way to look at this. Define "satisfaction" to be the y variable and excellence to be the x variable for all subjects be they employees or customers. Add an indicator variable (ResponseType) to the data set identifying customers and employees.
Add any other covariates to the data set such as age, gender etc etc and analyze as a retrospective regression analysis.
Satisfaction = Excellence+RespndentType+Excellence*ResponseType + Other covariates
With this model you can test to see if Satisfaction is percieved to be related to excelllence
You can test to see if this perception varies among customers and employees (main effect of Response.
You can also test to see if the difference in perception between customers and employees varies with the level of excellence--the interaction term.
This seems like a very rich way to summarize these data and you can use all of the records.
In an earlier post, I stated that “If you don't have values associated with an individual for every single variable you include in your regression model, standard computer programs will drop all data for the individual out of the calculations.” Since software for standard (ordinary least squares or OLS) regression may not give you an explicit warning message that this has happened, I’ll use this post to describe and demonstrate what that looks like to the subject matter specialist using statistics.
As part of your regression analysis you will get a table of numbers that includes an overall p-value and individual p-values for each variable you included in your regression model. That table will also include a column of numbers labeled df or degrees of freedom. If you add up all the degrees of freedom on the table, the sum will be one (1) less than the total number of individuals (subjects, records, samples, organizations, …) used in calculating the regression (or other OLS ANOVA table). The unreported degree of freedom was used to calculate the overall average for the “y” variable. A simulation follows my signature with data vaguely similar to those discussed in this thread. The software used is R.
Again, I wish you much success in your research.
Chuck
Note that the following is best viewed by copying and pasting into something allowing the use of Courier or some other non-proportional font:
> # Demonstrated Effect of Missing Values in OLS Regression
> # Let es = Employee's Satisfaction
> # ee = Employee's Measure of Excellence
> # ce = Customer's Measure of Excellence
> # cf = Customer's Measure of Friendliness
>
> # Data are generated with measures of 1 to 5 equally
> # likely for all for variables.
> # Let satisfy1 = Dataset for all satisfaction measures
> # satisfy2 = satisfy1 with one measurement missing for cf
> es ee ce cf satisfy1 satisfy2 satisfy2[1,4]
> # Display the datasets
> satisfy1
es ee ce cf
1 4 3 3 2
2 1 4 2 3
3 3 5 3 1
4 1 4 3 5
5 4 4 2 4
6 3 1 1 3
> satisfy2
es ee ce cf
1 4 3 3 NA
2 1 4 2 3
3 3 5 3 1
4 1 4 3 5
5 4 4 2 4
6 3 1 1 3
>
> # OLS Model 1: Regression with Ordinary Least Squares (OLS)
> olsmod1 anova(olsmod1)
Analysis of Variance Table
Response: es
Df Sum Sq Mean Sq F value Pr(>F)
ee 1 0.4211 0.4211 0.1190 0.7630
ce 1 0.1570 0.1570 0.0444 0.8527
cf 1 1.6774 1.6774 0.4740 0.5623
Residuals 2 7.0779 3.5390
> # The sume of the Df (degrees of freedom) is the number of employees minus 1
>
> # OLS Model 2: OLS with a single missing covariate value
> olsmod2 anova(olsmod2)
Analysis of Variance Table
Response: es
Df Sum Sq Mean Sq F value Pr(>F)
ee 1 0.1565 0.1565 0.0280 0.8945
ce 1 0.9810 0.9810 0.1753 0.7476
cf 1 0.4656 0.4656 0.0832 0.8212
Residuals 1 5.5969 5.5969
> # Sum the Df. With a single missing covariate,
> # an entire employee record is removed from OLS calculations.
Mahfuz, my opinion is that if your intention is to make a regression, you have first to identify your explanatory variable and your dependent variable. Job satisfaction is a clear dependent variable. But "excellence" seems to be more of a "constant" than a "variable". So as not to complicate your regression analysis, you must enter only the paired values- making both variables with equal sample sizes.
In my opinion first you make the observations equal by various imputations techniques available. Then apply regression if you realty interested in predicting the dependent variable based on predictor variable.
sample size for independent and dependent variables should be same. If you could not impute then ignore that point. This I told you in my last post also.. There is other way of employing the technique Take job satisfaction as categorical variable say yes or no. If your other variable is quantitative and you are really want to predict then you can also apply logistic regression instead of plain regression. If you just want to see the difference the you can also apply the t test taking group variable to be job satisfaction.
Mahfuz, the answer to your question has been well motivated by the other contributors. We have to remember that regression is mainly used to predict change in the dependant variable. In other words a certain "level of excellence" must predict a certain level of job satisfaction. To me excellence is an abstract construct. Can one be more excellent/ less excellent. I will depending on your research question an hypotheses use ANOVA, t-test or Z-test
But what will be the difference if the possibility of a missing value made the observation (sample) of dependent variable and independent variable(s) not equal
I am regressing the students' academic achievement with their trust in teachers. However, the number of students who expressed their level of trust in teachers (sample =327) and the academic result of students of the whole class . Which type of regression is recommended ?
if one leader evaluate the performance of team employees and other hand 3 4 employees of same leader evaluate the behavior of leader......"The responses of 319 salespeople and 102 of their matched team leaders were retained in the final sample pool". In this case the sample size is different both of them. then how code the data in SPSS.?
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