Concepts of Latent and Manifest Variables Paper Example

Introduction

Different effects may be analyzed and evaluated for instance, the number of people intermarrying from other races. These are perfect indicators of how bad or good the leadership of a country is. The better the leadership, the more the number of these items or indicators. These statistics about the kind of leaders elected is considered to be the reflective indicators since they are reflection of the leadership; patterns of peaceful forum conducted can be considered as formative indicators since they are perceived or ought to contribute to the quality of leadership.

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As you can imagine satisfaction, usability, motivation, and peace are only four instances of uncountable number of other many concepts that is not possible to measure directly. It is crucial to face the truth that the variables that we are interested in our models cannot be measured or observed directly. These concepts are designated a special name of latent variables though they are also called composites, constructs, theoretical concepts, vague concepts, factors, and intangibles. The variables are usually common in behavioral sciences and social sciences like sociology, psychology, and economy in which they exist several concepts of theoretical nature. For example, psychology talk of commitment, intelligence, and self-esteem. Sociologists normally refer to social stratification, social structure, and social status. Economists talk of economic development, utility, and organizational performance. Though it is also possible to find entities in the biological sciences that cannot be observed. For instance, in ecology, we might come across concepts such as territory quality, soil fertility, and habit structure.

The important part we work with constructs and theoretical concepts including developing models and theories, we end up conceiving anticipated casual relationships on theoretical concepts or constructs. The president of a certain country can propose new policies to reduce inter-tribal wars. People of different races decide to intermarry to reduce racism and enhance peace. A diplomat encourages international relations among the developing countries. Countries decide to form the regional pact that will enhance peace in a certain region.

The above actions give the courses of actions are normally undertaken because of including at theoretical concepts. The president believes that changing the country policies will accelerate peace in the country which in turn make people to live in harmony. There exist hypothetical variables, theoretical concepts which are difficult or impossible to measure or observed. The constructs are regarded as a data reduction device help in summarizing several numbers of variables into little factors. They are considered to be underlying factors that assist in the explanation of the relationship of at least two observable variables (Lohmoller, 2017). Toy model is usually typical of the structural model. Defining a simple model based on a useful theory, the better the quality of leadership, and the quality of the international relationship, the more peace will prevail. The theory involves two hypothesis, one is if the leadership of the country improves then people will live in harmony and peace will prevail. The other hypothesis is that if the international relations is enhanced then countries will have good relations and therefore more peaceful. The theory can be expressed in a form that is more abstract such as; Peace=f{leadership, international relations}. This is conceptual to means that peace is a function of leadership and international relations. Though we can go further and specify a linear function and express our theory by use of the equation: Peace =b1leadership +b2internatioall relations.

It is possible to display the model in the form of a graphical model known as path diagram. The diagrams assist in the representation in a visual way the associations stated in the models

Manifests Variables

The benefit of latent variables is that it not possible to measure them directly, it does not imply that they are useless or nonsense. To make latent variables operatives, they are measured indirectly by means of other variables which can be observed or measured perfectly. These variables are known as manifests variables and are denoted by MVs, also known as items or indicators. The assumption we have is that manifest variables have information that indicates or reflect each aspect of the construct; therefore we use the data contained in items or indicators to estimate representation of the latent variable.

Reflective and Formative indicators

After assuming that it is possible to measure latent indirectly by using manifest variables, we need to put into consideration the methods by which latent variables are measured indirectly. Measuring latent variables in two ways is possible. Through their effects or consequences shown on their indicators. Through other different indicators which are assumed to bring about the latent variables

For instance, in the initial case, known as a reflective way, we consider latent variables to cause manifest variables. In the second case called a formative away since the items or the indicators must form the latent construct. The main difference between formative and reflective ways has to do with relationships of casual-effect involving the constructs and the indicators. Different effects may be analysis and evaluated, for instance, the number of people intermarrying from other races. These are perfect indicators of how bad or good the leadership of a country is. The better the leadership, the more the number of these items or indicators. These statistics about the kind of leaders elected is considered to be reflective indicators since they are a reflection of the leadership; patterns of peaceful forum conducted can be considered as formative indicators since they are perceived or ought to contribute to the quality of leadership (Henseler, 2017).

NOTATION

Let have the assumption that we have p variables observed on n observations and p variables can be subdivided into j-blocks. We will apply the following notations: X represents the data sets containing p variables and n observations. X is a matrix having dimension n*p. X can be subdivided into j, mutually exclusive blocks including x1, x2.....xj, and each block Xu contain k variables. The estimation or approximation of latent variables, also referred to as LVdj=Y usually denotes the score (Henseler, 2013).

Structural MODEL

There are three things to put into considerations in inner relationships

1. Linear relationships - the initial aspect of the inner model is to that every structural relationship as linear relationships (Hulland, 2014). The structural relationships can be expressed in mathematical notation

LVj = v0 + X I vjiLVi + errorj

Where the subscript on LVi directly refers to the latent variables which are to be predicted. Bji is the path coefficient, and they are the representations of the direction and strengths of the relations between the predictors LVi and the LVj. v0 refers to the intercept term, and errorj represents the residuals (Henseler, 2015).

2. Recursive Models. The second thing to take note of is that the systems of equations ought to be the recursive system. In simple terms, the paths that are followed by the arrows of the inner model should not form any loop.

3. Regression Specification. The other aspect about the inner specification is something we referred to as predictor specification and is a fancy term to express linear expression concept. The concept about this specification is that the linear relationships are derived from a standard perspective E (LVj |LVi) = v0i + X ij vjiLVi

The extra assumption is cov (LVj, errorj) = 0

Which imply that LVj is not correlated with the residual error term j. There are nothing we notices about the distributions of the error terms and the variables, what is needed is the existence of second and first order moments appearing in the variables (Hair, 2014).

Concept of Weight

All the latent equations and all the latent variables and the assumptions considered directly depend on the latent variables LVj though the problem is that they are virtual entities. The weight relations bridge the gap existing between the material LVs and the virtual LVs (Henseler, 2015). The latent variables in PLS-PM are approximated as a linear combination of the particular manifest variables. In additionLVj is known as a score, which can be denoted as Yj: LVdj=Yj= X KWJKxJK. The latent variables are computed as a weighted sum of their items or indicators. It is essential to confuse the role of score Yj and the role that LVj plays. They both refer to the same factor while the latter is mainly used for theoretical reasons, the former is used mainly for practical reasons. It does not matter whether the latent variable is observed in a formative or reflective way, a latent is computed as a linear combination of indicators.

There are several ways to calculate the internal weights: - centroid scheme (Wold): Il centroid scheme is the scheme of the original algorithm by Wold. This scheme considers only the direction of the sign among the latent variables, without considering neither the direction nor the power of the paths in the structural model.

PLS Algorithm

Stage 1

Inner approximation and outer approximation to approximate the parameter. PLS considers two double estimations for LVs

Stage 2

External estimation or the outer approximation. It is used for measurement of models. In the stage we get the first proxy of each LV, being a linear combination of its MVs

Stage3

The internal approximations are also referred to as a structural model. The relations among LVs are considered to find the proxy of every LVs of its adjacent LVs. The internal approximation is computed as the product of the inner weights and the external estimation (Chin, 2018). There are three main ways of calculating the internal weights.

Centroid scheme (wold)

The centroid schema also is known as Wold: The scheme of original series of steps by wold is centroid schema. The schema is a consideration of the direction of the sign among the variables with no consideration of the power nor the direction of the paths in the structural model.

The factorial schema also is known as Lohmoller; the schema makes use of the correlation coefficients like internal weights not using the correlation signs. Hence it considers both the power of the link and direction of a sign in the structural model.

The path weighting scheme

The latent variables are subdivided into followers and predictors regarding the cause-effect relations occurring between the two latent variables,

BOOTSTRAP AND CLUSTERING

Since the PLS-PM does not depend on the distributional assumptions, resampling techniques are used to get the information about the parameters estimates variability. Plspm () offers bootstrap resampling to obtain the confidence intervals for evaluation of the precision of the estimates. Since we are satisfied with the outcomes, we can go on with the process of bootstrap validation

References

Chin, W. W. (2018). The partial least squares approach to structural equation modeling. Modern methods for business research, 295(2), 295-336.

F. Hair Jr (2014). Partial least squares structural equation modeling (PLS-SEM) An emerging tool in business research. European Business Review, 26(2), 106-121.

Hair, J. F. (2017). An assessment of the use of partial least squares structural equation modeling in marketing research. Journal of the academy of marketing scie...