Using a maximum of two pages, single-sided (12 font):Explain what is the regression surface methodology (RSM).

On polynomial regression and regression surface analysis

It is very common to use difference score to measure fit in organizational research. For example, Edwards and Cable (2009) hypothesized that congruence between personal and organizational values is positively related to communication among employees, attraction and trust . If individual values match with organizational values, e.g., employees value relationships and the organization values relationships as well, positive work outcomes would result.

One can then measure the importance of different values to individual employees (to make it simple, we assume that there is only one value dimension, called x), as well as importance of the same value dimension to the organization as perceived by the employee (y). A difference score measure means that (x-y) is used as a simple representation of value-fit between individual employee and the organization, and is used to predict the organizational outcome, e.g., trust (z). In sum, (x-y) is hypothesized to be positively related to z.

Jeff Edwards, in his classical paper (Edwards & Parry, 1993) criticized this approach of using difference score to measure value fit between employees and the organization. The logic is simple and strict forward. Using the symbols stated above, the difference score prediction equation can be summarized as follows:

(1)

Note: (x-y)2 is used instead of simply (x-y) because the misfit when x>y is the same as a misfit when y>x. If we expand this equation, we get:

(2)

Equation (2) is a second-order linear equation (i.e., second-degree polynomial). If we follow the tradition in statistics that when higher order terms are included in the model, all lower order terms should be included as well, Equation (2) can be represented as a special case of a general second order equation:

(3)

Comparing Equation (3) and Equation (2), one can see that the difference score model (Equation 2) artificially imposed three constraints:

Assignment

Using a maximum of two pages, single-sided (12 font):

(1) Explain what is the regression surface methodology (RSM).

(2) Without graphing the regression surface diagrammatically, explain how RSM can be used to test the following hypotheses given a dataset of x, y and z:

H1: A congruence of an employee’s personal relationship orientation (x) and the organization’s culture of relationship orientation (y) is positively related to employee’s commitment to the organization (z).

H2: When employees’ values (x) is congruent with the organization’s values (y), the stronger the values, the higher is the commitment of the employees to the organization.

What calculations are needed?

What do they mean?

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