Reflective and Formative Constructs

The second generation of statistical modeling namely Structural Equations Modeling (SEM)  distinguishes two measurement models: reflective and formative latent measurement constructs (Edwards & Bagozzi, 2000).

In reflective construct, the construct is the cause of the items designed to measure the construct. In other words, the items can reflect the concept in the construct. However, all the items meant to reflect the construct are expected to be correlated and, therefore, some of them can be deleted without affecting the concept in the construct.

As an example, if job satisfaction construct is defined to be measured as a reflective construct, then one can use items such as

•   I like my job.
•   I’m happy in my work,
•   I am unlikely to want to leave this position. As illustrated in Figure 1

 

 

Figure 1: Reflective Construct

On the other hand, in the formative construct, the items are the causes of the construct. Meaningthat, the items meant to measure the construct form the concept in the construct. These items, however, might not be correlated and, therefore, deleting any item(s) may cause that some of the construct aspects are ignored. 

For example, if job satisfaction construct is conceptualized as a formative construct, one can use items such as

•     I am satisfied with my pay,
•    I have a good boss
•     My work hours are ideal.
•   I have many promotion opportunities.
•   I enjoy working with my co-workers,….and so on as illustrated in Figure 2

 

Figure 2: Formative Construct

As a researcher, the first and most important step is to clearly define what we are planning to measure and whether our construct is to be defined reflectively or formatively BEFORE designing a questionnaire or generating items or questions. Specifically, we have first to establish a clear conceptual definitions of our constructs and plan how we are going to measure them.

Reference

Edwards, J. R., & Bagozzi, R. P. (2000). On the nature and direction of relationships between constructs and measures. Psychological Methods, 5, 155-174.

Latent and Observed Variables

The Observed Variable:

It is the variable that can be measured or observed directly such as age and income.

Latent Variable, or sometimes called unobserved variable:


It is defined as the concept or construct that cannot be measured or observed directly. Rather, it is measured through some other variables called manifest, indicators, or items. Variables such as Motivation and Job satisfaction. For the purpose of measuring the hidden concept, items or questionnaire questions are to be prepared and answered by the respondents. 

The observed variables, directly measured, can be used to measure the latent variable, indirectly measured as illustrated in the following figure. 

                                  Source: Google Image

Introduction to Structural Equations Modeling Using AMOS Graphics

Assalamualaikum/ Greetings.

 

In collaboration between Awang Had Salleh Graduate School of Arts and Sciences and Quantitative Research Clinic, we will be organizing Postgraduate Enhancement Series 15: Introduction to SEM AMOS Workshop.

 

The details of this workshop are as follows:

This workshop is limited to 20 persons only. The closing date for registration is on 19 June 2013.

Registration can be made by filling the form attached and bring the form or fax the form (04-9285975) to the Dean’s Office of Awang Had Salleh Graduate School of Arts and Sciences on/before 19 June 2013. You may also scan the form after filling it and send to this e-mail, m.asman@uum.edu.my.

 

For further enquiries, please contact Asman (04-9284935,e-mail: m.asman@uum.edu.my)  or Mieja (04- 9285972).

Awang Had Salleh Graduate School of Arts and Sciences

College of Arts and Sciences

Universiti Utara Malaysia

Univariate and Multivariate Normal Distribution

Normal (or Gaussian) distribution is a continuous distribution, defined by a probability density function as in the following

Where μ is the mean and it is also the median and mode (for normal distribution mean=median=mode). The parameter σ is its standard deviation; its variance is therefore σ². A random variable is said to be normal if it has he normal distribution.

                                   The red curve is the standard normal distribution

                                Source: Wikipedia

If the normal distribution has the zero mean and the unity as the standard distribution, it is called a standard normal distribution.

A variable that is normality distributed will have the bell shape distribution in which less than one standard distribution from the mean around 64.2 % of the data as in the dark blue area in the following shape. That is, the normal variable is that the majority of the data, 64.2 %, lies around the mean. Around 91.4% of the data lies in less than 2 times the standard deviation from the mean.  In three times the standard 95.6% of the data are located. 

                                         Source: Wikipedia

The generalization of the univariate normal distribution is known as the mulltivariate normal distribution or multivariate Gaussian distribution. It is often used to describe a set of correlated random variables the values of which are centered around their respective  mean values. The Probability Density Function is given by the following. 

Remember:

In a multivariate system: univariate normal distribution is a necessary but not sufficient condition of Multivariate normal distribution. In other words, if we have a multivariate normal distribution, the marginal distribution of each dimension is univariate normal. 

The normality assumption is a must for hypotheses testing in parametric statistics.