Evaluating direct, indirect, and total effects in path analysis in AMOS

in this video I'm going to discuss how to generate and test indirect and total effects using the Amos program we're going to focus on path analysis with measured variables but the same concepts will generalize in terms of path analysis with latent variables path analysis both with and without latent variables can include several types of effects that can be of interest to the researcher there's what's called the direct effect which is basically the effect of one variable on another and it's indicated by the single headed arrow so for instance the path from X to Y in this particular model with which is designated with the letter A is a direct effect a direct effect of X on Y similarly the path from Y to Z is a direct effect and that's path B the same would go down here a and B are both reflecting direct effects the first one reflecting the effect of X on Y the second one reflecting the effect of Y on Z we also have another direct effect which is I just have a little C star right here but basically it reflects the direct effect of X on Z so a single headed arrow reflects a direct effect in a path model now another type of effect is referred to as an indirect effect and in this case we are looking at the issue of mediation and when we're talking about mediation we're talking about the idea that the variation in one variable on our the effect of one variable on another variable is transmitted through another variable a third variable or an intervening variable so in this case right here the effect the indirect effect or the mediated effect of X on Z flows through variable Y and this is a mediating variable so the indirect effect is calculated by taking the path coefficient for a and multiplying it by this path coefficient for B so so in this case the the effect of X on Z again is going through why the second model model to down here we have the indirect effect of X on Z flowing again through Y or at least partially through Y where we have Pat's a and path B so again Pat a x path B would constitute the indirect effect of X on Z so in both of these models right here the indirect effect of X on Z is calculated at Pat a coefficient times path B coefficient now an indirect effect can partially or fully explain the relationship between two variables and know when I talk about explain I mean it in terms of the proposed causal Association so in model one we can see that the effect of X on Z is it's full in other words are the indirect effect is full so because basically there's no other relationship between X and Z all of the causal influence of X on Z flows through variable right so in this case right here Y would be which is the mediating variable is proposed to fully explain the relationship between X and Z now in model two we have a partial mediation model and in this case right here the effect of X on Z flows in part through Y which is our proposed mediator so again the indirect effect is calculated as path a times Pat B coefficients but we also have what's called a direct effect between X and C in this case there is no proposed mediation here but part of the influence of X on C is direct a lot of times this just sort of reflects the idea that we don't have any other proposed mediators in that case the only other option in terms of specifying the relationship between X and Z is direct whereas in this part of the model we have a proposed intervening variable or mediating variable and so the the effect of X on Z is partial through the end in direct effect and then partially direct so the total effect of one variable on another is basically equal to the sum of all indirect effects and direct effects within a model so for model 1 the total effect of X on Z is basically equal to the indirect effect on Z which is taking path coefficient a and multiplying it by path coefficient B in model 2 we have both an indirect effect of X on Z through the mediator Y and we also have a direct effect of X on Z which is the C star path so to calculate the total effect of X on Z we simply take the product of a and B which is the indirect effect and some are added to the direct effect which is passed seed that we see right here so in path analysis in Amos basically we you know here's an example of a model and basically we are modeling both direct and indirect effect so the effect in this particular model of performance goals on achievement is completely indirect as we have one arrow going to anxiety another error going to from anxiety the mediator to achievement and so as you can see there's no direct path that flows from performance goals to achievement so so the the effect of performance goes on achievement is only indirect this with respect to the mastery and interest variables we have mastery exhibiting a direct effect on anxiety and and obviously anxiety to achievement as the direct effect but basically part of the effect of mastery on achievement is indirect that is we take this path coefficient right here multiplied by this path coefficient here and that would give us the indirect effect that you in this particular model but we also have the direct effect of mastery on achieve as well so in other words we're specifying a partial mediation with respect to the relationship between mastery and achievement part of the effect is direct part of the effective indirect was again going back to performance goals the proposed relationship between that variable and achievement is completely indirect through anxiety similar to the mastery predictor variable we also have interest which is proposed to exhibit a direct effect on achieve but then also an indirect effect through the anxiety mediating variable so to run our analysis you know we will go into analysis properties and we have to essentially lay out direct indirect and total effects so if we go into our analysis properties in this particular video this is based on a complete set of data so there's no missing values on any of our variables and so we would not be clicking this intercept estimate means in intercepts box if we did have missing data than we would want to click this so to ask for the direct indirect or Total Effects we'll go to output and under this box right here I've already asked for standardized estimate squared multiple correlation test for normality outliers but then here's the box indirect directed Total Effects so basically to illustrate this in action I'll just go ahead and run this analysis so here we are under analysis properties I'm going to ask for output and I'm going to ask for indirect direct and total effects ok so so that's what I need right there so I'm going to click off of that and really quickly save and click on calculate estimates and basically there was a little error I had to re-upload the data into the file so we've done that and that's so now I'm going to go ahead and click and so when I go to my little output box right here I will click on estimates and so basically all of the direct effects that we had the model so I can actually click over here and just kind of show you these are the unstandardized estimates these these passcode chants are all reflecting the direct effects in the model so if I want to look at the tests of the direct effects in the model I can look at the unstandardized regression weights that's what these are right here so you can see here the the values are rounded to two decimal places in the output here it's rounded to three but basically you can see that we have a the regression weight here standard error and then the critical ratio is basically formed as a ratio of the estimate divided by the standard error and typically we would given that SEM tends to be a large sample procedure we compare this against Z values in the Z table so the p value or the probability value is indicates whether or not we have statistical significance so you can see in this particular model we got performance goal to anxiety that path here is zero but basically it's point zero zero four it's not actually zero but you can see that path is not statistically significant at the 0.05 level when we see mastery two anxiety you can see it's negative 0.4 so in other words higher scores on this variable are associated with lower scores on anxiety the estimate here you can see it was rounded off right here and so we end up with negative point three nine eight and the three asterisks here is basically it's considered a p-value less than point zero there one so that path was statistically significant then in terms of mastery to achieve this direct effect right here which you see right here is a statistically significant higher scores on mastery goals are associated with higher scores on achievement and then we have interest to achievement as well this path was positive and statistically significant if we want to look at the standardized estimates for those paths we can just click on that if we want if we want to look at in terms of our output here you can see these are the standardized weights basically these would be the beta coefficients in the context of a standard of regression analysis so the nice thing about beta weights is that we can form comparative judgments about you know which effects in the model are larger versus smaller so you can see that the path from and so we interpret the size or the magnitude of the effects in terms of their absolute values so you can see mastery it has a negative predictive relationship with anxiety has a positive relationship with achievement the larger effect would be this one right here with mastery running to achievement with the beta coefficient of 0.38 whereas the next largest effect is this one where master is running to anxiety beta coefficient negative 0.3 for the next largest effect runs from interest to achievement with a beta coefficient of point two nine so that's basically how we can use that we can't use the unstandardized weight or the regression coefficient excuse me in order to judge relative relative size of effects because these are in the original units of measurement for our variables but the standardized regression weights we can use these because essentially this is after we've converted all of our variables to have a mean of zero a standard deviation of 1 so given we have the same scale of measurement we can make comparative judgments here that we can't make when we're looking up here at the unsanitized coefficients so if we go down a little bit further we you know we you can get down to matrices total effects we have so these are unsere as total effects standardized total effects unstandardized direct effects standardized direct effects unstandardized indirect effects and standardized indirect effects I could also get there by clicking on this little button right here and clicking on matrices and it will take me you know to whatever I want to look at so you can go either way so for our purposes for our analysis let's say I want to look at the indirect effect of of let's say mastery on achieve so this case we have the past so I'm going to go to my own standardized just for the time being and in this particular case if I take this path coefficient here negative point 4 and multiply it times negative 0.04 then the indirect effect of metrion achieve down here this is the unstandardized would be point zero one six and so basically as you can see that's that's the value I want to look at the indirect effect of interest on achieve I would take this this path right here point o one and multiply times negative 0.04 and you'll see that it comes out at negative point zero zero one if I do the same in terms of the standardized coefficients you can see that basically in this case I would be looking at these coefficients down here so mastery to achieve basically if I take mastery negative point three four multiplied times negative 0.05 I would end up with point zero one H and the other one he love interest to achieve 0.01 times negative 0.05 and I would end up with approximately negative point zero zero one you can see performance goes to anxiety to achieve as well be 0.04 times negative 0.05 and that would give me the negative 0.02 these are actually very small effects and you know in terms of making judgments about the size of the effect or the relative size of the effects then you would probably want to look at the standardized indirect effects in terms of making comparative judgments about which indirect effects were larger relative to others so in this river models the indirect effect of mastery on achievement is the largest followed by the performance goal on achievement by interest on achievement you'll notice that anxiety it says anxiety to achievement right here is 0 there is no indirect effect that's why there why that value in here is zero so also whenever there's no indirect effects then all the other values would end up being equal being zero we have interest - anxiety in this particular model you can see obviously there's no indirect effect it's only a direct effect and so there's zero here and the same would go for the other predictors in relation to anxiety the direct effects that you see right here the unstandardized and the standardized indirect effects those values are going to basically equal the unstandardized and standardized regression coefficients that you see in this particular table so it's not particularly useful to look at the direct effects in this particular table you can but it's just going to tell you the same thing as what we saw up above if you want to talk about the the total effects there's a total in the total the unstandardized total effects and then we have the standardized total effects that you see right here so now let's say I want to modify things and let's say I want to look at let's say I include another mediator let's let's make interest a mediator both interesting anxiety mediators between let's say mastery and achieve so I've got mastery predicting anxiety mastery predicting interest and both of these are influencing achievement in this project model so really quickly I'll draw draw this out I'll just pull up that particular model that we see right here and in this particular case there it is so I'm going to now run the analysis and I'd actually perform the bootstrap on this I'm going to undo this for right now and I'll show you this distant second so again I'm going to click on indirect directed total effects run the analysis and so when I look at my output / estimates I can I can either scroll down all the way or I could just double click here and I get my scheme my [Music] matrices I got my different effects that I was just telling you about so basically as we're looking at the the indirect effects again here are the unstandardized values in this particular figure right here and so the unstandardized indirect effect of mastery on achievement in this particular case it's important to note that this basically is taking mastery to achievement and it's summing up to two routes so it's basically taking this coefficient here multiplying it by this coefficient here and then it's taking this coefficient here and multiplying it by this here and then summing those two indirect effects together to give you basically a total indirect effect so the total indirect effect of mastery on achievement is point what excuse me is 0.1 7/8 the unstandardized indirect effect so keep in mind that this value right here is not breaking it out into each individual route from mastery to achievement but rather is taking the total indirect effect for with respect to both of these mediators that you see in this particular model and some programs are able to isolate the indirect effect in terms of individual or trace particular paths and talk to you about those individually but in this particular case and Amos you're not really able to do that but you are still able to talk about the indirect effect of mastery on achievement just by taking the sum of both of these the products for these two paths here and these two paths right here so that's just something that I think it's important that you keep in mind when you are running your analysis so if I want to look at the standardized indirect effect for mastery goals again I would be taking the product of these two paths and summing it to the product of these two paths right here and says the indirect effect the standardized indirect effect would be 0.196 with respect to mastery and achievement remember that basically in this particular case the total effect whether we're talking about the unstandardized total effect are they standardized is basically reflecting then three total up to three effects and some there are two indirect effects mastery to achievement by anxiety mastery to achievement by interest and then also a direct effect that you see right here so basically if we sum this direct effect plus the total effect of the total indirect effect we end up with the total effects that you see in this matrix in this matrix now one last thing I want to mention is you know perhaps you want to determine if any of the indirect or total effects are statistically significant can you do this well yes you can right now if you just look at the the values that are printed out in the table all you're really able to do is to sort of identify the values and then with the standardized either total of standardized total effects or the standardized indirect effects or standardized direct effects right matter you can make comparative judgments about these effects at this level but if you want to determine statistical significance with respect to one of these effects then if you can do this through the use of bootstrapping and Amos so to do that we will click on analysis properties and go to bootstrap and that's where you run the bootstraps basically bootstrapping involves treating your sample data as sort of a pseudo population and you draw random samples with replacement from your your sample data because you're essentially trying to simulate data that would come from a given population you draw random samples of the same sample size as your original sample and and then essentially compute your estimates and rates or a sampling distribution for your standard errors that's basically how it works so to do this in Amos first of all one thing to note is that this button cannot be clicked so in other words if you have any missing data whatsoever in your analysis you then you're going to deal with the missing data problem first by completing a complete data set or generating a complete data set and this cannot be clicked otherwise it's not going to work so you know if I if I click this right now even and let's say I want to as for bootstrap results for you know if I click on calculate estimates you know well it actually did work but generally speaking well actually it will still run if you click on estimate means intercepts but if you if you have missing data you have to click on this and then if you have that missing data at all in your data set and it's not going to generate the bootstrap results so that's just kind of FYI but I actually had no missing data in this data set so I'm just going to leave this unclick so basically you have to have a complete data set that means that there can be no missing values on any of your variables in your analysis if there are missing values then that forces you to click this otherwise you'll get a nice little error message and then if you try to run the bootstrap it's just not going to work so just kind of keep that in mind but given that I don't have any missing data in my current data set I'm going to leave this clicked off which will allow me to generate my bootstrap samples and generate the standard errors and the test results that I need in order to test the indirect effects for statistical significance just kind of as a side note if you do have missing data and you need to generate a complete data set there are various ways that you could do that one way is you know through a deletion method like this wise deletion in which case if you have missing data on any variables in your data set you delete those cases that have missing data on at least one of those variables the downside of this approach is that it reduces your effective sample size and potentially if there is some systematic reason why there's missing data then you can end up skewing or biasing your sample your um your results another option is some type of imputation method such as you know regression imputation or stochastic regression imputation evasion and imputation these are some of the options that are available in Amos I'm not really going to go into that for this particular review but just to say that there are some options there to create a complete data set that you can then feed into Amos and then run the analysis and generate the bootstrap results so at any rate under bootstrap I'm going to click on perform bootstrap so typically it's you know the default it looks like this the default in here are actually 200 here for number of bootstrap samples and 90 here for 90 percent confidence intervals but I actually clicked this before and change the values to 595 so that you get 500 bootstrap samples and 95% bias corrected confidence interval so now I'm going to click on OK and I'm just going to go and resave my little file here and generate and click on calculate estimates so basically in this particular case when I look at my output I could click on estimates and again if I double click here click on matrices I've got you know all my different types of effects so basically if I click on let's say I want to look at the indirect effect if I click on this right here then down here this little estimates bootstrap section highlights so right now these are the estimates for the end the unstandardized indirect effect of mastery on achievement is point one seven eight if I want to test this for statistical significance then I can click on bootstrap confidence and so in this case right here I've got a 95% confidence interval for the relationship between mastery and achievement for the indirect effect or the interesting direct effect so basically the lower bounds of that interval rate is 0.07 for the upper bound point three one two and so basically if the null hypothesis for the indirect effect is that it is equal to zero so zero falls between the lower bound and the upper bound value then then the null hypothesis would be retained and which case we would say that the indirect effect is not statistically significant in this case zero falls outside of this these two bounds right here so then we would infer that the effect the indirect effect of mastery on achievement is statistically significant so you know if we want to look at this a little bit more in depth this is this is basically the 95% confidence interval for the unstandardized indirect effect of mastery on achievement and like I said zero falls outside that interval so we would reject a null we could also look at if we want to look look at a p-value then down here you've got p-values for two-tailed tests of significance and so the p-value for the indirect effect of mastery on achievement is point zero zero two so if we adopt a conventional 0.05 level for the test of the indirect effect we could say that the indirect effect was statistically significant for a model you know notice too that we you know we can look at things in similar way with the standardized indirect effect so we have the confidence interval for the standardized indirect effect ranges from 0.076 to 0.33 eight and so obviously zero is falling outside that bounds so we would reject and all there or if you want to look at the PV down here you can look at that and determine the standardized indirect effect is a statistically significant also you know I do want to note that we also have other options with respect to the regression weights that we saw up above that the bootstrap results don't only pertain to the indirect direct and total effects but well you know we have the direct effects right here but we can also look if we wanted to test the these unsanitized effects using the bootstrap method well there it is you actually have confidence intervals that are formed for the bootstrap direct effects in the model and then the p-values associated with that so you might use this option if there's some kind of question whether or not you have say for instance violations of multivariate normality and maybe you don't necessarily trust the normal theory estimates and tests that you have right here and you want to adjust for that then bootstrapping can be kind of helpful in those cases but at any rate that kind of sums up or provides an overview of looking at the different effects in the context of a path analysis using either observed variables or latent variables

Channel: Mike Crowson

Views: 77,656

Rating: 4.909091 out of 5

Keywords: AMOS, SPSS, path analysis, structural equation modeling

Id: MQR0kLXDqhk

Length: 29min 58sec (1798 seconds)

Published: Mon Feb 13 2017