What is Structural Equation Modeling?
You have an empherical data of a set of variables. A causal relationship exists between the variables in the data set. In other words there is a path that exists between the variables in the data set.
SEM is all about studying that path that exists between the variables .
You create a hypothesis determining the relationship between the variables and then statistically test if the hypothesis is true or false.
A Theoretical model is created with defined paths and then this path is tested on the actual data to verify if the path specified by you is true or false.
Hence chi square test is used in the analysis to examine the difference between the 2 variables –a comparison of theoretically expected values to the predicated values.
Since the Null Hypothesis is something which has to be accepted in this case unlike other cases, the model with a very high p value (greater than 0.05) is always considered to be the best model, higher the difference between the two variables higher is the value of the chi square, and the model with a high chi square value is always rejected, because the intention is to prove that the model which you have specified is the best model.
Hence a model with a low Chi-Square value and a very high P Value is considered to be the best Model.
Analytical Technique:SEM is a combination of Factor Analysis, Analysis of Variance and Regression Analysis.
Factor Analysis:Factor analysis is a statistical technique which is basically used to describe the variability among the constructs by a potentially lower number of unobserved variables called as factors.
You can also use these factors as independent variables in the Model.
Analysis of Variance:The Analysis provides the data to check whether or not the means of several groups are equal or not.
Significance test used in ANOVA is F Statistics:
When you want to test the difference between the means of two groups then we use a T –Test .When you want to compare the means of more than 2 groups then we use One –Way Analysis of variance.
Difference between one way ANOVA and two way ANOVA!
Between the Groups Eg.,in a clinical trial design of experiment – when we have only one factor - treatment effect which has to be tested between the groups then we use one –way ANOVA but when we have to capture 2 effects simultaneously– treatment effect and time effect then we use 2 way ANOVA.
T test is same as ANOVA- when conducted on two groups as both will yield same results.ANOVA on two groups or T test yield the same results.
Why conduct ANOVA and why not simple T Test?
Two way ANOVA is conducted with more than 2 groups in the design of experiment with more than one independent variable .Why not conduct a simple T test instead of ANOVA is a question?
The error rate we specify in a t test is 0.05. When we conduct multiple t tests on different groups – the error will be greater than 0.05 (alpha selected) – it’s called as family error .Hence TWO way ANOVA is conducted when there are more than 2 groups and more than one independent variable -we ignore the T Test here because of the accuracy in the results .
Two Types of variance is measured in ANOVA.
Between Group Variance – MS Group (Mean Squared Deviation)
Within Group Variance – MS Error (Chance Error)
Significance is tested with F Statistics = MS Group / MS Error
Instead of T Statistic – we use F Statistics.? Why Is a question?
Because statisticians are very smart – they want to show off., others should feel that “what the hell is he talking about????????? Iam almost kidding! Its no Rocket Science.
Its simple college mathematics. Personally iam not a statistics graduate, Although i learnt business statistics for 5 years as one of my module -My major was finance and Risk Analytics
F is named after Sir Ronald Fisher who studied agricultural statistics and he said and proved that F Test with 2 groups is nothing but T Test, you will get same results with either.
F Test:
Null hypothesis: µ1= µ2=µ3= µk(Means of all groups are same)
Alternate Hypothesis:µ1≠µ2≠ µ3≠ µk
Steps in SEM :
1.Develop Hypothesis:
2.Construct a Path Diagram
Paint the Relationship between the variables/Constructs
3.Create a Model Structure :
Identify the rules - Errors should not be correlated with each other , errors should also be un-correlated with each other.
4. Identify a Model Structure:
Check if the metrics can be solved: Check if we have enough data or are we missing any data. Do we create any Dummies for the missing data? Calibration and Estimation of missing data points with a logic/Business Sense.
Examine the correlation between the variables to check how far x and y resembles a straight line- if one variables increases other also increases.
Examine a sample – to check if you get the same correlation –coefficient to see if the sample represents the population.
Do as many as iterations as possible
A higher Chi-Square indicates that there
is a big difference . A high chi-square will have low P Value.
Other measures of Model Evaluation:
Although iam not interested in other Model Evaluation Techniques , i have a screen shots for the readers in case if they want to analyze further.
Evaluation of Results :
Modification of the Model
Include new path, add new variable if required to make the model more significant.
You have an empherical data of a set of variables. A causal relationship exists between the variables in the data set. In other words there is a path that exists between the variables in the data set.
SEM is all about studying that path that exists between the variables .
You create a hypothesis determining the relationship between the variables and then statistically test if the hypothesis is true or false.
A Theoretical model is created with defined paths and then this path is tested on the actual data to verify if the path specified by you is true or false.
Hence chi square test is used in the analysis to examine the difference between the 2 variables –a comparison of theoretically expected values to the predicated values.
Since the Null Hypothesis is something which has to be accepted in this case unlike other cases, the model with a very high p value (greater than 0.05) is always considered to be the best model, higher the difference between the two variables higher is the value of the chi square, and the model with a high chi square value is always rejected, because the intention is to prove that the model which you have specified is the best model.
Hence a model with a low Chi-Square value and a very high P Value is considered to be the best Model.
Analytical Technique:SEM is a combination of Factor Analysis, Analysis of Variance and Regression Analysis.
Factor Analysis:Factor analysis is a statistical technique which is basically used to describe the variability among the constructs by a potentially lower number of unobserved variables called as factors.
You can also use these factors as independent variables in the Model.
Analysis of Variance:The Analysis provides the data to check whether or not the means of several groups are equal or not.
Significance test used in ANOVA is F Statistics:
When you want to test the difference between the means of two groups then we use a T –Test .When you want to compare the means of more than 2 groups then we use One –Way Analysis of variance.
Difference between one way ANOVA and two way ANOVA!
Between the Groups Eg.,in a clinical trial design of experiment – when we have only one factor - treatment effect which has to be tested between the groups then we use one –way ANOVA but when we have to capture 2 effects simultaneously– treatment effect and time effect then we use 2 way ANOVA.
T test is same as ANOVA- when conducted on two groups as both will yield same results.ANOVA on two groups or T test yield the same results.
Why conduct ANOVA and why not simple T Test?
Two way ANOVA is conducted with more than 2 groups in the design of experiment with more than one independent variable .Why not conduct a simple T test instead of ANOVA is a question?
The error rate we specify in a t test is 0.05. When we conduct multiple t tests on different groups – the error will be greater than 0.05 (alpha selected) – it’s called as family error .Hence TWO way ANOVA is conducted when there are more than 2 groups and more than one independent variable -we ignore the T Test here because of the accuracy in the results .
Two Types of variance is measured in ANOVA.
Between Group Variance – MS Group (Mean Squared Deviation)
Within Group Variance – MS Error (Chance Error)
Significance is tested with F Statistics = MS Group / MS Error
Instead of T Statistic – we use F Statistics.? Why Is a question?
Because statisticians are very smart – they want to show off., others should feel that “what the hell is he talking about????????? Iam almost kidding! Its no Rocket Science.
Its simple college mathematics. Personally iam not a statistics graduate, Although i learnt business statistics for 5 years as one of my module -My major was finance and Risk Analytics
F is named after Sir Ronald Fisher who studied agricultural statistics and he said and proved that F Test with 2 groups is nothing but T Test, you will get same results with either.
F Test:
Null hypothesis: µ1= µ2=µ3= µk(Means of all groups are same)
Alternate Hypothesis:µ1≠µ2≠ µ3≠ µk
Result
1.Big F and Small P (LESS
THAN 0.05) = Accept Alternate Hypothesis and reject Null Hypothesis
2.Small F and Big P (GREATER THAN
0.05) = don’t reject Null Hypothesis.
Our goal is to accept the
Null Hypothesis .
Steps in SEM :
1.Develop Hypothesis:
Develop a relationship between the
variables/Constructs. Independent Variables are called as Exogenous Variables
Dependent Variables are known as Endogenous
Variables.
Specify the Structural Model after examining the
relationship
2.Construct a Path Diagram
Paint the Relationship between the variables/Constructs
3.Create a Model Structure :
Identify the rules - Errors should not be correlated with each other , errors should also be un-correlated with each other.
4. Identify a Model Structure:
Check if the metrics can be solved: Check if we have enough data or are we missing any data. Do we create any Dummies for the missing data? Calibration and Estimation of missing data points with a logic/Business Sense.
5.Parameter
Estimation :
Examine the correlation between the variables to check how far x and y resembles a straight line- if one variables increases other also increases.
Examine a sample – to check if you get the same correlation –coefficient to see if the sample represents the population.
Do as many as iterations as possible
6.Parameter Estimation :
Measurement Model
A Factor
Analysis will examine the relationship between the variables – by unobserved
underlying factors.Try to study the relationship thats existing between the
variables to prove that your hypothesis is very true
7.Parameter Estimation :
Structural Model
Factors can also be used as independent
variable.
Path Co-efficient = Regression weight =
standardized regression co-efficient.
8.Model Evaluation: Chi Square Test The chi-squared
distribution is used in the common chi-squared tests for goodness of fit of an
observed distribution to a theoretical one,
We have a theoretical structure with
defined paths with theoretical distribution and then the actual predicted
values - another distribution . Chi-Square compares these 2 distribution to
check if there is a difference .
Chi Square calculates the independence
between 2 variables and compares theoretically expected values by the path defined by us ) vs. the
empherical data.
The bigger the difference – sooner the
Chi-Square becomes significant .
Since we are dealing with Mis –Fit issue
here – we need to be careful while examining the model statistics.
The P Value should be insignificant here.
Other measures of Model Evaluation:
Although iam not interested in other Model Evaluation Techniques , i have a screen shots for the readers in case if they want to analyze further.
Evaluation of Results :
T value and Chi Square Difference Test .
Modification of the Model
Include new path, add new variable if required to make the model more significant.
An SEM Song ! Yes a Song!
Gotta Fix It to 1
Lyrics by Alan Reifman
(May be sung to the tune of "Fortunate Son," John
Fogerty)
(Dr. Reifman, lead vocals)
You make a construct, with its loadings,
Can’t let them, all be free,
So that the model’s identified,
Fixing one is the key,
It ain’t free,
It ain’t free,
Gotta fix it to 1,
It ain’t free,
It ain’t free,
In AMOS, automatically done
The number of knowns in your model,
The unknowns can’t exceed,
Fixing a loading for each construct,
Will accomplish this need,
It ain’t free,
It ain’t free,
Gotta fix it to 1,
It ain’t free,
It ain’t free,
In AMOS, automatically done
Another Song on Structural Equation
Modeling
Parsi-Mony
Lyrics by Alan Reifman
(May be sung to the tune of "Mony Mony,"
Bloom/Gentry/James/Cordell)
Structural models need parsimony,
Don’t want to add paths that are phony,
Put the paths you need, now that’s all right, now,
You got to keep your model lean and tight, now,
...lean and tight now,
Yeah, yeah, yeah…
If you can account (PARSIMONY),
For (PARSIMONY),
The data (PARSIMONY),
With a (PARSIMONY),
Minimum of paths (PARSIMONY),
You’ve got (PARSIMONY)
You’ve got (PARSIMONY)
You want parsimony ...mo ...mo ...mony,
Parsimony ...mo ...mo ...mony,
Parsimony ...mo ...mo ...mony...
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