To gauge motivation score?

Question

In order to gauge the level of motivations of my respondents to connect in Second Life, I have proposed to them to answer (with a Likert scale - 7 points: from totally disagree to totally agree) to 16 statements (items) that I have categorized myself in four motivation categories.

For example the fulfillment motivations

1. The fact that my avatar gains a higher status (in terms of money, material possessions, reputation, etc) is important to me. (HIGH STATUS)
2. The fact that Second Life allows me to undertake and make money is important to me (START BUSINESS)
3. The fact that Second Life allows me to gain valuable knowledge in the virtual world (scripting language, etc) and / or in the real world (to follow courses in Second Life, etc) is important to me. (TO ACQUIRE KNOWLEDGE)
4. The fact that Second Life allows me to create whatever I want is important to me. (CREATE)
5. The fact that Second Life allows me to be altruistic (helping new residents, …) is important to me. (BE ALTRUISTIC)

I would like to compute the average score of each respondents the fulfillment motivation

           HIGH STATUS|START BUSINESS|TO ACQUIRE KNOWLEDGE|CREATE|BE ALTRUISTIC| 
Resp n°29        4             6             6          7         6        5,8
Resp n°30        2             4             6          6         4        4,4
Resp n°31        5             7             4          1         5        4,4

In place of computing a simple arithmetic average I envisage a principal component analysis If I do a PCA for the 5 assesments of the fulfillment motivations : Principal components/correlation Number of obs = 373 Number of comp. = 4 Trace = 5 Rotation: (unrotated = principal) Rho = 1.0000

--------------------------------------------------------------------------
   Component |   Eigenvalue      Difference         Proportion      Cumulative
-------------+------------------------------------------------------------
       Comp1 |      2.72909            1.81017              0.5458            0.5458
       Comp2 |      .918928           .121757               0.1838            0.7296
       Comp3 |      .797171           .242364               0.1594           0.8890
       Comp4 |      .554806           .554806               0.1110           1.0000
       Comp5 |  4.44089e-16            .                       0.0000            1.0000
--------------------------------------------------------------------------

Principal components (eigenvectors)

--------------------------------------------------------------------
    Variable    |   Comp1   Comp2  Comp3   Comp4 | Unexplained 
-------------+----------------------------------------+-------------
Statut_Elevé    |   0.2544    0.8212   -0.4932    0.1330 |            0 
Lancer_Bus      |  0.5549   -0.3110   -0.2713   -0.1475 |            0 
Créer   |   0.4279    0.0046    0.4411    0.7889 |            0 
Altruisme   |   0.3693    0.3637    0.6442   -0.5625 |            0 
Acquérir_C      |   0.5549   -0.3110   -0.2713  -0.1475 |            0 
--------------------------------------------------------------------

I was wondering if I could not sort my items in both components:

 Resp n° 29
 Comp1:     (0.2544*4)+(0,5549*6)+(0,4279*7)+(0,3693*6) + (0,5549*6) = 12,8875  
 Comp2:   (0,8212*4) + (-0,3110*6) + (0,0046*7) + (0,3637*6) + (-0.3110 *6) = 1,7672

And after computing the mean of both components : 7,32735

Is this approach appropriate? If not, what can I do better than simple average items to calculate a score of achievement motivation?

Answer 1

There are a number of problems in there and nobody will be able to tackle everything in a short answer or spare you the trouble of learning and reading about whatever techniques you end up using. Your description also raises many questions and is not entirely clear.

Generally speaking, it would seem common to directly analyze the original items (without “parcelling”), aiming at recovering the hypothesized dimensions (e.g. “be altruistic” or “start a business”) and use and interpret the resulting scales scores. Also, since you seem to be trying to extract measures of some latent constructs like “altruistic motivation”, factor analysis would seem more appropriate than PCA.

You can find a lot of relevant material on this site but Factor analysis of questionnaires composed of Likert items seems particularly relevant.

In any case the following paper should directly address the specific question you formulated at the end:

• DiStefano, C., Zhu, M., & Mîndrilă, D. (2009). Understanding and Using Factor Scores: Considerations for the Applied Researcher. Practical Assessment, Research & Evaluation, 14 (20).