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.

How to Download and Install SmartPLS

Steps To Download and Install SmartPLS

1.      Initiate the SmartPLS website

 2.      Register  in the SmartPLS website by filling in your particulars and submit

 3.      Within three days after registration, a key will be sent to you that can be used to activate the software after it has been downloaded.

 4.      Every three month, the website management will ask you to provide a new key that can be generated from the website as in the following

Good questionnaires are difficult to construct; bad questionnaires are difficult to analyze.

The questionnaire designed to collect the data of the study is the instrument that should be calibrated and its validity and reliability should be examined before it is to be used. This implies rigorous methodology to study the existing literature and review the available measures and exert a great attention to the development and the assessment of the questionnaire.

That is why GOOD QUESTIONNAIRE IS DIFFICULT TO CONSTRUCT.

The data generated based on ill-developed questionnaire will have low quality and may not be useful to the phenomenon under investigation. In addition, the conclusions drawn based on that will be poor and lack the reliability and validity.

That is why BAD QUESTIONNAIRES ARE DIFFICULT TO ANALYZE.   

KMO and Bartlet’s Test in Factor Analysis

Question:

How to use KMO and Bartlett's Test to Check Whether or not the Factor Analysis can be applied to my Data? 

 Answer:

Kaiser-Meyer-Olkin measure of sampling adequacy and Bartlett's test of sphericity are very important measures to conclude the worthiness of factor analysis. KMO takes values between 0 and 1. A value of 0 indicates that the sum of partial correlations is large relative to the sum of correlations, indicating diffusion in the pattern of correlations and the factor analysis is not appropriate to be conducted. A value close to 1 indicates that patterns of correlations are relatively compact and so factor analysis should yield distinct and reliable factors. 

In other words, KMO indicates the amount of variance shared among the items designed to measure a latent variable when compared to that shared with the error. Kaiser (1974) recommends accepting values greater than 0.5 as acceptable. More specifically, values between 0.5 and 0.7 are considered mediocre, values between 0.7 and 0.8 are considered good, values between 0.8 and 0.9 are deemed great and values above 0.9 are superb (Hutcheson and Sofroniou, 1999). A value more than 0.7 is the common threshold for confirmatory analysis (Hair et al., 2010).

Before being able to run the factor analysis, one should ensure that the data has an adequate level of multicolinearity, the multicolinearity issue is not desirable in regression analysis but it is a prerequisite here. Bartlett's measure tests the null hypothesis that the original correlation matrix is an identity matrix.

H₀:The Correlation Matrix= I(Identity Matrix)

H₁: The Correlation Matrix≠ I(Identity Matrix)

The identity matrix is the matrix in which all the diagonal elements are ones and the off diagonal elements are zeros. Meaning that there original data has no correlations among its variables.

Factor analysis cannot be performed on the data for which the correlation matrix is the identity matrix. Therefore, we want this test to be significant (i.e. has a significance value less than 0.05). If the P value is less than 0.05 we have to reject the null hypothesis thus there are some relationships between the variables we considered in the analysis.