Moderators: With moderation, a third variable impacts or interacts with the relationship between two other variables. We would say the relationship between two variables is ‘moderated.’ This can be thought of as an interaction in a standard regression:
Y = b0 + b1*X1 + b2*X2 + b3*X1*X2
b3 =moderating effect i.e. the relationship between Y and X1 changes with levels of X2
b1 = impact of X1 on Y when X2 = 0.
So in the context of the relationship between Y and X1, X2 is a moderator
Mediators: With mediation, a third variable invervenes in the relationship between two other variables. For example, in the diagram below, suppose we are interested in the relationship between x and y. This relationship may be ‘mediated’ by a third variable m.
Consider a model where Y = grade in course (our outcome of interest), k = IQ, m = study skills. We might hypothesize that study skills ‘mediate’ the effect of IQ on course grade. A perfectly brilliant person might do OK on an exam through educated guesses, but we all might know of cases where brilliant students have done quite poor due to lax study skills. So while there may be a direct effect of IQ on grades, IQ -> grades or x -> y there is an indirect effect as well, IQ->Study Skills -> grade or x -> m -> y.
This implies that mediation can take a number of forms and can be formally tested. In the case of full mediation, the relationship between x and y becomes insignificant after a mediator ‘m’ is included in the model, or our estimate of c (modeling the path or direct effect between x and y) isn’t significantly different from 0. Partial mediation would occur if the relationship between x and y or c is reduced (but remains significant) after m is entered into the model). In this case we could say that x has both direct effects on y (through the path c) as well as an indirect effect (through the mediator m or paths a and b).
These relationships can be formally tested as laid out in Hair et al:
1) Test for significant correlations between x,y or estimate c; x,m or estimate a; m,y or estimate b
2) If c is significant after m is included, and the magnitude of c does not change then m is not a mediator.
3) If the magnitude of c is reduced after including m, and c remains significant, then m is a moderator. This is a case of partial mediation.
4) If including m in the model reduces the magnitude of c such that it is not significantly different from 0, then m is a mediator and this is considered a case of full mediation.
Reference: Multivariate Data Analysis. 6th Edition. Harris, Black, Babin, Anderson and Tatham. Pearson-Prentice Hall. 2006.
An attempt to make sense of econometrics, biostatistics, machine learning, experimental design, bioinformatics, ....
Showing posts with label SEM. Show all posts
Showing posts with label SEM. Show all posts
Tuesday, January 10, 2017
Monday, April 14, 2014
Perceptions of GMO Foods: A Hypothetical Application of SEM
So how can we best quantify these ‘latent’ constructs or
‘factors’ that may be related to perceptions of biotechnology, and how do
we model these interactions? This
will require a combination of techniques involving factor analysis and
regression, known as structural equation modeling. We might administer a
survey, asking key questions that relate to one’s level of monsantophobia, science knowledge, and political views. To the extend that ‘monsantophobia’
exists and shapes views on biotechnology, it should flavor responses
to questions related to fears, skepticism, and mistrust of ‘big ag.’ Actual
knowledge of science should influence responses to questions related to science etc.
We also may want to quantify the actual flavor of perceptions of GMO food. This
could be some index quantifying levels of tolerance or preferences related
to policies concerning labeling, testing, and regulation or purchasing decisions and expenditures on related goods. To the extent that perceptions are ‘positive’ the index would reflect that on some scale related to answers
to survey questions about these issues. You could also include a set of questions related to policy preferences and try to model the interaction of the above factors and their impact on the support for some policy or the general policy environment.
Suppose we ask a range of questions related to skepticism of
big ag and agrochemical companies and record the responses to each question as
a value for a number of variables (Xm1…Xmn), and did the
same for science knowledge (Xs1…Xsn), political ideology
(Xp1…Xpn), and overall GMO perception (Yp1…Ypn) and policy environment (Ye1…Yen) .
Given the values of these variables will be influenced by the actual latent
constructs we are trying to measure, we refer to the X’s and Y’s above as
‘indicators’ of the given factors for monsantophobia, science, politics, gmo perception, and policy environment. They may also be referred to as the observable manifest variables.
Now, this is not a perfect system of measurement. Given the level of subjectivity among other things, there is likely to be a
non-negligible amount of measurement error involved. How can we deal with measurement error and quantify the
factors? Factor analysis
attempts to separate common variance (associated with the factors) from unique
variance in a data set. Theoretically, the unique variance in FA is correlated
with the measurement error we are concerned about, while the factors remain
‘uncontaminated’ (Dunteman,1989).
Structural equation modeling (SEM) consists of two models, a
measurement model which consists of deriving the latent constructs or factors
previously discussed, and a structural model, which relates the factors to one
another, and possibly some outcome. In this case, we are relating the factors
related to monsantophobia, science, and political preferences to the outcome,
which in this case would be the latent construct or index related to GMO
perceptions and policy environment. By using the measured ‘factors’ from FA, we can quantify the
latent constructs of monsantophobia, science, politics ,and GMO perceptions
with less measurement error than if we simply included the numeric responses
for the X’s and Y’s in a normal regression. And then SEM lets us identify the relative influence of each
of these factors on GMO perceptions and perhaps even their impact on the general policy environment for biotechnology. This is done in a way similar to regression, by
estimating path coeffceints for the paths connecting the latent constructs or factors as depicted below.
Equations:
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References:
Principle Components Analysis- SAGE Series on
Quantitative Applcations in the
Social Sciences. Dunteman. 1989.
Awareness and Attitudes towards Biotechnology Innovations
among Farmers and Rural Population in the European Union
LUIZA TOMA1, LÍVIA MARIA COSTA MADUREIRA2, CLARE HALL1, ANDREW BARNES1, ALAN RENWICK1
Paper prepared for presentation at the 131st EAAE Seminar ‘Innovation for Agricultural Competitiveness and Sustainability of Rural Areas’, Prague, Czech Republic, September 18-19, 2012
LUIZA TOMA1, LÍVIA MARIA COSTA MADUREIRA2, CLARE HALL1, ANDREW BARNES1, ALAN RENWICK1
Paper prepared for presentation at the 131st EAAE Seminar ‘Innovation for Agricultural Competitiveness and Sustainability of Rural Areas’, Prague, Czech Republic, September 18-19, 2012
A Structural Equation Model of Farmers Operating within
Nitrate Vulnerable Zones (NVZ) in Scotland
Toma, L.1, Barnes, A.1, Willock, J.2, Hall, C.1
12th Congress of the European Association of Agricultural Economists – EAAE 2008
Toma, L.1, Barnes, A.1, Willock, J.2, Hall, C.1
12th Congress of the European Association of Agricultural Economists – EAAE 2008
PLoS One. 2014; 9(1): e86174.
Published online Jan 29, 2014. doi: 10.1371/journal.pone.0086174
PMCID: PMC3906022
Determinants of Public Attitudes to Genetically Modified Salmon
Latifah Amin,1,* Md. Abul Kalam Azad,1,2 Mohd Hanafy Gausmian,3 and Faizah Zulkifli1
Published online Jan 29, 2014. doi: 10.1371/journal.pone.0086174
PMCID: PMC3906022
Determinants of Public Attitudes to Genetically Modified Salmon
Latifah Amin,1,* Md. Abul Kalam Azad,1,2 Mohd Hanafy Gausmian,3 and Faizah Zulkifli1
Friday, April 11, 2014
Structural Equation Models, Applied Economics, and Biotechnology
Toma gives some nice descriptions of SEM methodology and application:
Awareness and Attitudes towards Biotechnology Innovations among Farmers and Rural Population in the European Union
LUIZA TOMA1, LÍVIA MARIA COSTA MADUREIRA2, CLARE HALL1, ANDREW BARNES1, ALAN RENWICK1
Paper prepared for presentation at the 131st EAAE Seminar ‘Innovation for Agricultural Competitiveness and Sustainability of Rural Areas’, Prague, Czech Republic, September 18-19, 2012
SEM may consist of two components, namely the measurement model (which states the relationships between the latent variables and their constituent indicators), and the structural model (which designates the causal relationships between the latent variables). The measurement model resembles factor analysis, where latent variables represent ‘shared’ variance, or the degree to which indicators ‘move’ together. The structural model is similar to a system of simultaneous regressions, with the difference that in SEM some variables can be dependent in some equations and independent in others.
A Structural Equation Model of Farmers Operating within Nitrate Vulnerable Zones (NVZ) in Scotland
Toma, L.1, Barnes, A.1, Willock, J.2, Hall, C.1
12th Congress of the European Association of Agricultural Economists – EAAE 2008
To identify the factors determining farmers’ nitrate reducing behaviour, we follow the attitude-behaviour framework as used in most literature on agri- environmental issues. To statistically test the relationships within this framework, we use structural equation modelling (SEM) with latent (unobserved) variables. We first identify the latent variables structuring the model and their constituent indicators. Then, we validate the construction of the latent variables by means of factor analysis and finally, we build and test the structural equation model by assigning the relevant relationships between the different latent variables.
See also:
PLoS One. 2014; 9(1): e86174.
Published online Jan 29, 2014. doi: 10.1371/journal.pone.0086174
PMCID: PMC3906022
Determinants of Public Attitudes to Genetically Modified Salmon
Latifah Amin,1,* Md. Abul Kalam Azad,1,2 Mohd Hanafy Gausmian,3 and Faizah Zulkifli1
Awareness and Attitudes towards Biotechnology Innovations among Farmers and Rural Population in the European Union
LUIZA TOMA1, LÍVIA MARIA COSTA MADUREIRA2, CLARE HALL1, ANDREW BARNES1, ALAN RENWICK1
Paper prepared for presentation at the 131st EAAE Seminar ‘Innovation for Agricultural Competitiveness and Sustainability of Rural Areas’, Prague, Czech Republic, September 18-19, 2012
SEM may consist of two components, namely the measurement model (which states the relationships between the latent variables and their constituent indicators), and the structural model (which designates the causal relationships between the latent variables). The measurement model resembles factor analysis, where latent variables represent ‘shared’ variance, or the degree to which indicators ‘move’ together. The structural model is similar to a system of simultaneous regressions, with the difference that in SEM some variables can be dependent in some equations and independent in others.
A Structural Equation Model of Farmers Operating within Nitrate Vulnerable Zones (NVZ) in Scotland
Toma, L.1, Barnes, A.1, Willock, J.2, Hall, C.1
12th Congress of the European Association of Agricultural Economists – EAAE 2008
To identify the factors determining farmers’ nitrate reducing behaviour, we follow the attitude-behaviour framework as used in most literature on agri- environmental issues. To statistically test the relationships within this framework, we use structural equation modelling (SEM) with latent (unobserved) variables. We first identify the latent variables structuring the model and their constituent indicators. Then, we validate the construction of the latent variables by means of factor analysis and finally, we build and test the structural equation model by assigning the relevant relationships between the different latent variables.
See also:
PLoS One. 2014; 9(1): e86174.
Published online Jan 29, 2014. doi: 10.1371/journal.pone.0086174
PMCID: PMC3906022
Determinants of Public Attitudes to Genetically Modified Salmon
Latifah Amin,1,* Md. Abul Kalam Azad,1,2 Mohd Hanafy Gausmian,3 and Faizah Zulkifli1
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