We did an Experience Sampling study and collected data (events, emotions, work engagement) from 55 people twice a day for nine working days (repeated measures design: daily measures are nested in individuals). We like to test a moderated mediation model with: Daily events --> triggering emotional experiences (mediator) --> influencing work engagement (DV) (Lower Level Mediation). The moderators are on Level 2 (they were measured once). Is it possible to test such a multilevel moderated mediation model with Mplus and how could I perform the analyis? Thanks a lot in advance!
Yes, it is possible. Bauer, Preacher, & Gil (2006, pp. 153-158) address this model. We have code in SAS, SPSS, and HLM for lower-level mediation models with the potential for moderation by level-2 predictors (see quantpsy.org), but it is also easy to do in Mplus. Here is Mplus code that yields the same output:
TITLE: 1-1-1 model from BPG article DATA: FILE IS bpg_example_data.dat; VARIABLE: NAMES ARE id x m y; CLUSTER IS id; ANALYSIS: TYPE = TWOLEVEL RANDOM; MODEL: %WITHIN% sa | m ON x; sb | y ON m; sc | y ON x; m y; %BETWEEN% sa sb sc m y; sa WITH sb(cab); sa WITH sc m y; sb WITH sc m y; sc WITH m y; m WITH y; [sa](sa); [sb](sb); [sc](sc); MODEL CONSTRAINT: NEW(ind); ind=sa*sb+cab; ! indirect effect OUTPUT: TECH1 TECH8;
Bauer et al. use a parametric bootstrap to obtain a CI for the indirect effect. A modification of the R code here can be used to achieve the same goal using Mplus output. Ex.11.11 in the Mplus Users Guide will also be helpful.
Bauer, D. J., Preacher, K. J., & Gil, K. M. (2006). Conceptualizing and testing random indirect effects and moderated mediation in multilevel models: New procedures and recommendations. Psychological Methods, 11, 142-163.
Thanks a lot! Especially the Mplus code was very helpful.
Jeffrey Kahn posted on Wednesday, November 16, 2011 - 8:52 am
I have a 2-1-1 mediation model based on a diary study. Event rumination mediates the relation between attachment anxiety and event disclosure. Attachment avoidance is a level 2 covariate predicting event disclosure. Event intensity is a moderator of the b path between event rumination and event disclosure.
My Mplus code is based on Preacher, Zypher, and Zang (2010):
TITLE: Moderated mediation model DATA: FILE IS data.dat; VARIABLE: NAMES ARE code ev_int ev_disc ev_rumin attavoid attanx; USEVARIABLES ARE code ev_int ev_disc ev_rumin attavoid attanx; BETWEEN IS attanx attavoid; CLUSTER IS code; ANALYSIS: TYPE IS TWOLEVEL RANDOM; MODEL: %WITHIN% ev_rumin ev_disc; sb | ev_disc ON ev_rumin; %BETWEEN% attanx ev_rumin ev_disc attavoid; ev_rumin ON attanx(a); ev_disc ON ev_rumin(bb); ev_disc ON attanx attavoid; sb WITH attanx ev_rumin ev_disc attavoid; [sb](bw); MODEL CONSTRAINT: NEW(b indb); b=bb+bw; indb=a*b; OUTPUT: TECH1 TECH8 CINTERVAL;
Did I handle the attavoid covariate properly? Also, how do I integrate the moderating effect of ev_int? Thanks.
With a significant sb slope your model specification in your first message gives an interaction between the within-level part of ev_rumin and the between-level part of ev_disc. This, I think, is the moderation you talked about in your first message.
See also slide 45 of our Topic 7 short course handout.
Yan Liu posted on Monday, April 30, 2012 - 11:46 am
I am conducting some anlayses using the multilevel mediation models based on SEM framework introduced by Preacher, Zyphur, and Zhang (2010). I also read the paper "constructing covariates in multilevel regression" by Asparouhov and you (2007).I like this new approach a lot.
However, I found that the model doesn't run for ordinal categorical outcome variable. I wonder if there is a way for me to use this approach for categorical outcome.
The model I used has two outcomes (PAHome & PESch), one mediator (Enjoy) and one predictor (TT). The syntax is attached as follows.
Yan Liu posted on Thursday, May 03, 2012 - 4:44 pm
Thank you for your reply. I tried WLSMV estimator, then the model worked fine. Do you think if this is appropriate?
If it is, I have further questions. First, as far as I know full information ML can handle missing data. Here I used WLSMV, how are the missing data handled using this estimator?
Second, for my data set 20% missing on the mediator and two outcome variables. The missing values depend on gender and the predictor(a latent variable with four indictors). Is my understanding correct that I should include gender as a covariate to control for the gender differences on missingness (for both mediator and outcome variables)?
Can I use gender as a moderator? I tried to create an interaction between gender and the predictor (latent variable), but it didn't work. Is there a way to do it?
See the following technical appendix on the website:
Weighted Least Squares Estimation with Missing Data
Yes, you should include gender as a covariate. You can use the XWITH option to create an interaction between a latent an observed variable.
Yan Liu posted on Wednesday, May 09, 2012 - 6:19 pm
Thank you so much! So WLS estimator still uses FIML to treat missing values. What is the default for deleting missing values? I noticed the number of observations in the output is the same as the covariate, gender.
I tried the interaction between "gender" and the latent predictor "TTw", but it seems WLSMV doesn't run for this moderated mediational model. The error message is "WLSMV is not allowed with TYPE=RANDOM". So do we have to use MLR estimator?
Hence, I changed estimator to MLR, but it seems that the model didn't run if the outcome, "PESch", is defined as categorical. The error message is as follows.
Observed variable on the right-hand side of a between-level ON statement must be a BETWEEN variable. Problem with: ENJOY
I also tried to define the outcome "PESch" as a continuous variable, but it doesn't work well. If I have to treat outcome variables as continuous to run moderated mediational models, what strategies would you recommend? Thanks a lot!
Here is part of my Mplus syntax. ANALYSIS:TYPE = TWOLEVEL RANDOM; MODEL: %WITHIN% TTw BY ideal-individ; sexTT| sex XWITH TTw; Enjoy ON TTw (aw); Enjoy ON sex sexTT; PAHome ON Enjoy (b1w); PAHome ON TTw sex sexTT; PESch ON Enjoy (b2w); PESch ON TTw sex sexTT;
Missing data handling is not done in the same way for weighted least squares and maximum likelihood. Weighted least squares is described in the technical appendix I referred you to. Maximum likelihood is described in the Little and Rubin book cited in the user's guide.
Missing data theory applies to dependent variables. Observations with missing data on one or more independent variables are not included in the analysis.
Yan Liu posted on Wednesday, May 16, 2012 - 12:27 pm
Followed your suggestion, I put a factor behind enjoy, but it seems the model didn't work. Could you please take a look and see if my model is specified correctly. Thanks a lot! Yan
ANALYSIS: TYPE = TWOLEVEL RANDOM;
MODEL: %WITHIN% TTw BY ideal-individ; sexTT| sex XWITH TTw; fw BY enjoy@1; enjoy@0; fw ON TTw (aw); fw ON sex sexTT; PAHome ON fw (b1w); PAHome ON TTw sexTT; PESch ON fw (b2w); PESch ON TTw sexTT;
%BETWEEN% TTb BY ideal-individ; fb BY enjoy@1; enjoy@0; fb ON TTb (ab); PAHome ON fb (b1b); PAHome ON TTb; PESch ON fb (b2b); PESch ON TTb; ideal-individ@0;
Here is the error message. THE ESTIMATED WITHIN COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. THE VARIANCE OF TTW APPROACHES 0. FIX THIS VARIANCE AND THE CORRESPONDING COVARIANCES TO 0, DECREASE THE MINIMUM VARIANCE, OR SPECIFY THE VARIABLE AS A BETWEEN VARIABLE.
The message says that the variance of ttw approaches zero. To investigate why, you could simplify the model to only include the ttw and ttb factors, that is, using only the variables ideal-individ. If that does not show the same problem, then add variables into that model. Step-wise model building is always recommended.
Ari Malka posted on Saturday, June 09, 2012 - 4:39 pm
We are testing a model wherein we have military personnel nested within teams. Each team also has a group of leaders (and a group of subordinates). We have hypothesized a moderated-mediation model wherein Leadership Team Cohesion --> Subordinate Team Cohesion --> Team Performance. We also hypothesized two first stage moderators: (1) subordinate level of agreement on the extent to which their leadership team forms a cohesive unit and (2) racioethnic similarity between the leadership and subordinate teams (in the same larger team). We want to use moderated-mediation wherein all variables are at level 2 and wherein all variables are at level 1 (except the moderators) all in the same model. In other words, we want to have 6 latent variables (3 team level and 3 individual level). Is this possible?
Yes, you can have a model with 3 team-level and 3 individual-level latent variables.
ari malka posted on Saturday, June 30, 2012 - 12:00 pm
Thanks for the response above (regarding the model with leadership team cohesion). I am having trouble figuring out the code for mediation (both levels 1 and 2)and the code for the two moderators. Would it help to see my model? What is the best way for me to show it to you? Any help would be greatly appreciated!!
ari malka posted on Saturday, June 30, 2012 - 12:01 pm
So far, this is my code:
VARIABLE: NAMES ARE Cluster ClusSize Rank SubTeam Gender Race Age TeamEff1 TeamEff2 TeamEff3 TeamEff4 TeamCoh1 TeamCoh2 TeamCoh3 TeamCoh4 LeadCoh1 LeadCoh2 LeadCoh3 LeadCoh4 RaceSim rwgTCun rwgLCun; USEVARIABLES ARE ClusSize Rank SubTeam Gender Race Age TeamEff1 TeamEff2 TeamEff3 TeamEff4 TeamCoh1 TeamCoh2 TeamCoh3 TeamCoh4 LeadCoh1 LeadCoh2 LeadCoh3 LeadCoh4 RaceSim rwgTCun rwgLCun Cluster; MISSING ARE ALL (999); CLUSTER IS Cluster;
ANALYSIS: TYPE IS TWOLEVEL; ESTIMATOR IS MLM; ITERATIONS = 1000; CONVERGENCE = 0.000001;
Model: %Within% LTCi by LeadCoh1@1 LeadCoh2 LeadCoh3 LeadCoh4; TCi by TeamCoh1@1 TeamCoh2 TeamCoh3 TeamCoh4; TPi by TeamEff1@1 TeamEff2 TeamEff3 TeamEff4; TCi on LTCi; TPi on TCi;
%Between% LTCg by LeadCoh1@1 LeadCoh2 LeadCoh3 LeadCoh4; TCg by TeamCoh1@1 TeamCoh2 TeamCoh3 TeamCoh4; TPg by TeamEff1@1 TeamEff2 TeamEff3 TeamEff4; TCg on LTCg; TPg on TCg;
OUTPUT: SAMPSTAT RESIDUAL STANDARDIZED CINTERVAL TECH3 TECH4; SAVEDATA: FILE IS Diss Data for Mplus 6.22; FORMAT IS FREE; RECORDLENGTH = 1000;
baozhenzhou posted on Friday, January 31, 2014 - 8:23 pm
Hello! We want to test a moderated mediation model just like the model 5 in the following paper (when the a and b paths are both moderated by w): Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42, 185-227. Our model is perceived school climate (x) --> deviant peers affiliation (m) --> delinquency(y). The moderator is effortful control (w). Given we were analyzing clustered data (students are nested within 10 schools). Is it possible to test such a multilevel moderated mediation model with Mplus and how could I perform the analyis? Thanks a lot in advance!
Ten schools is too few for multilevel modeling. You need at least 20 and many would suggest 30-50. Instead create nine dummy variables and use those as covariates to control for non-independence of observations.
baozhenzhou posted on Saturday, February 01, 2014 - 6:32 pm
Linda, thanks for your help! The Mplus User's Guide has a description of how to refer the levels of a nominal dependent variables in the MODEL command but no description of how to create dummy variables for independent in the DEFINE command. I have searched the Mplus Discussion for the answers and found the following example. But I still can't understand how to write the syntax for the dummy variables of 10 schools? Could you help me? Thanks a lot!
DEFINE; white = 0; if (raceth eq 1) then white = 1; black = 0; if (raceth eq 2) then black = 1; etc.
After a succesful multilevel mediation model (2-2-1), I'm looking for moderated mediation, using the Mplus codes that come with Preacher, Rucker and Hayes (2007) 'Addressing moderated mediation hypotheses'. I used model 2, where the a path is moderated by w (first stage moderation):
MODEL: %WITHIN% y on l;
%BETWEEN% y on m (b1) x w xw; m on x (a1) w xw (a3); MODEL CONSTRAINT: new (ind wmodval); wmodval = -1; ind=(a1+a3*wmodval)*b1;
Your help would be appreciated in the complete and correct interpretation of the findings: - m is significant to y, x/w/xw are not - x and w are significant to m, xw is not - significant indirect effect
In the above multilevel moderated mediation model with a categorical outcome, Mplus automatically uses Bayesian estimation. In a previous post in the 'CFA with Bayesian estimation' forum you mentioned that PPC for multilevel models has not been implemented yet. Is there a way to assess model fit here then?
Thanks for your reply! In my 2-2-1 model, I want to combine moderated mediation and simple mediation for another variable in the same model. Is the following model correct? Are there any problems known with such model, except that model fit cannot be assessed?
%BETWEEN% !moderated mediation y on m (b1) x1 w x1w; m on x1 (a1) w x1w (a3);
!mediation y on x2; m on x2(a);
MODEL CONSTRAINT: new (ind1 ind2 wmodval); wmodval = 0.125; ind1=(a1+a3*wmodval)*b1; ind2=a*b1;
Hi Dr. Muthen, I am wondering if mplus can test two moderators at different stages at the sometime, like model 21 in Hayes' new book "PROCESS". Basically, I want to test a model like this: x-->m-->y(y1, y2, y3), the relation between x and m is moderated by moderator 1, and m-->Y relation is moderated by moderator2. In addition, I also have multiple dependent variables.
Moreover, these y1, y2, y3 are measured by team leaders (all other variables are individual level), so I want to control for team level variance, so I specify a two-level model,just no independent variables in level 2.
So my questions are 1 can mplus test such a model? because I could use PROCESS macro in spss to test this moderated mediation, but PROCESS does not have multilevel functions. and it can only test one dv at a time.
2 if mplus can, can I use indirect to test the moderated mediation? Do I need to test each dv at a time? But can I use indirect to test two moderators at the same time?
Dear Dr. Muthen, I also have another model I am not quite sure. The model is a moderated mediation, x-->m(m1, m2, m3)-->Y(Y1, Y2, Y3), and the relation between x and m is moderated by a Moderator. All These variables are individual level, except for Y is measured by team leader, so i want to control for team level variance, but no IVs in team level. I have three mediators, and three dependent variables.
I have used Bayes iterations, and the moderation is significant. However, if I just use regular iterations, the results are not significant. My question is what is the difference between the two? Which results should I use?
This is possible in Mplus, but you have to study up on what it means. It is straightforward to do two-level moderated mediation in Mplus. In your case you just add a between part for the y variables by mentioning their variances. If Bayes gives significance and ML doesn't it can mean that the distribution of the estimate is not symmetric/normal. In this case Bayes is preferrable (bootstrap is an alternative for ML, but doesn't exist yet for two-level).
Yan Liu posted on Sunday, August 17, 2014 - 7:10 pm
Dear Dr. Muthen
I am trying a 2-1-1 multilevel moderated mediational model. However, I always got a error message to ask me to define cluster, which I have included (teacher's id). Could you please take a look at my Mplus syntax? Thanks a lot! (w=moderator, x=predictor,m=mediator, Sex=covariate, y1& y2=outcome)
DEFINE: xw=x*w; USEVARIABLES ARE x Sex w m y1 y2 tchid xw;
MISSING=ALL(999); CLUSTER = tchid; BETWEEN= x xw;
ANALYSIS: TYPE = TWOLEVEL RANDOM; STARTS=500; STITERATIONS=500;
MODEL: %WITHIN% m y1 y2; y1 ON Sex m; y2 ON Sex m;
%BETWEEN% x m y1 y2; mom ON Sex w x (a1) xw (a2); y1 ON Sex x xw w m (b1); y2 ON Sex x xw w m (b2); MODEL CONSTRAINT: NEW(ind1 ind2 wmodval); wmodval=-1; ind1=(a1+a2*wmodval)*b1; ind2=(a1b+a2*wmodval)*b2;
*** ERROR in VARIABLE command TYPE=TWOLEVEL requires specification for the CLUSTER option.
Currently you have CLUSTER=tchid in the DEFINE section. You may want to move the command "DEFINE: xw=x*w;" outside the VARIABLE section.
Yan Liu posted on Sunday, August 17, 2014 - 8:57 pm
Dear Dr. Preacher,
Thank you so much! It works!
I have one more question. I saw that wmodval is defined as -1 in an example (model 2) you provided in your paper (Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated Mediation hypotheses: Theory, methods, and prescriptions.)
What is this wmodval? How should we give the value to it?
wmodval is any value of the moderator at which you wish to estimate the effect of x on y. It could be the moderator's mean, the minimum or maximum, 1SD above the mean, etc. -- anything. You should look into the LOOP command in Mplus; it makes probing interaction effects easier.
Carolyn CL posted on Monday, August 25, 2014 - 9:15 am
I have one dependent level-1 variable(y), one level-1 independent variable(z), one level-1 mediator(m1), two level-2 mediators(m2_1, m2_2), and two level-1 controls(age and sex). I include both cross-level indirect pathways (1-1-1, 1-2-1, 2-2-1) and mediated moderation (interactions):
USEVARIABLES ARE ID y z m1 m2_1 m2_2 age sex zXm1 m2_1Xm2_2 zXm2_1 m1Xm2_2; CLUSTER = ID; BETWEEN = m2_1 m2_2 m2_1Xm2_2; DEFINE: zXm1 = z*m1; m2_1Xm2_2= m2_1*m2_2; zXm2_1= z*m2_1; m1Xm2_2= m1*m2_2; ANALYSIS: TYPE = TWOLEVEL RANDOM; MODEL: %WITHIN% y z m1 zXm1; y ON z m1 zXm1 age sex; m1 ON z age sex; %BETWEEN% y z m1 m2_1 m2_2 zXm1 m2_1Xm2_2 zXm2_1 m1Xm2_2; y ON z(a); y ON m1(b); y ON m2_2(c); y ON m2_1(d); y ON age sex zXm1 m2_1Xm2_2 zXm2_1; y ON m1Xm2_2(j); m1 ON z(e); m1 ON m2_2(f); m1 ON m2_1(g); m1 ON age sex; m2_2 ON m2_1(h); m2_1 ON z(i); m1 WITH m1Xm2_2; MODEL CONSTRAINT: NEW(INDgb INDfb INDeb INDsf xmodval); INDgb=g*b; INDfb=f*b; INDeb=e*b; xmodval = 1; INDsf=f+(b+j*xmodval);
Can you confirm that a sig coefficient for the m1Xm2_2(j) suggests a moderated mediated effect, but not an indirect effect (given non-sig INDfb term)?
In your model, a significant j coefficient suggests a significant interaction between m1 and m2_2 in the 'between' model, not moderated mediation, and not an indirect effect. Also, instead of:
I think you mean:
...which is the conditional indirect effect of m2_2 on y through m1, at the point where m2_2 = 1.
Carolyn CL posted on Monday, August 25, 2014 - 3:54 pm
Thank you for this.
A few follow up questions, if I may: 1) What can I make of a sig interaction, but no sig indirect or conditional indirect effects? 2) The estimated direct and indirect paths reflect unconflated estimates of within and between effects, with random intercepts? 3) Because I have very small cluster sizes (80% N =1, 20% N = 2-5), the within level of the model has very little power?
1) A n.s. indirect effect means that there is no evidence that the indirect effect departs from zero. A n.s. conditional indirect effect means that the effect in question does not detectably differ from zero at the chosen value of xmodval (but it might at others). The interaction's significance pertains only to the two interacting variables, and does not necessarily reflect the presence or absence of moderated mediation. We discuss how to quantify and test for the presence of moderated mediation for some models, including this one, in Appx. A of this paper (see Scenario 1). In your case, you can obtain a CI for f*j. If the CI excludes zero, that is evidence for moderated mediation.
2) You have no within effect of m2_2 on m1, only a between effect (f). There are both within and between effects of m1 on y, and only a between effect of the interaction term m1Xm2_2 (j). j is a strictly between effect, so all effects of interest are at the between level, and occur among level-2 variables and the random intercepts for the level-1 variables.
3) It is difficult to say without knowing more about your design and your expected effects. You can run a power analysis in Mplus, but because you already have the data it is probably too late to glean anything useful from a power analysis.
Carolyn CL posted on Wednesday, August 27, 2014 - 1:06 pm
Many thanks for this.
To be clear, the model now includes:
Y ON m1Xm2_2(j) !interaction effect INDfb = f*b !indirect effect effect of m2_2 on Y through m1 INDsf = f*(b+j*xmodval) !conditional indirect effect of m2_2 on Y, where effect through m1 depends on value of m2_2 INDjf = f*j !moderated mediation effect where strength of indirect effect of m2_2 on Y through m1 is moderated by m1
Carolyn CL posted on Wednesday, September 03, 2014 - 8:59 am
Dear Dr. Preacher,
I would like to obtain predicted values for the significant interaction term in my model.
I am unsure as to how to proceed in the MSEM framework and was hoping you would be able to provide me with a reference or formula to obtain predicted (fitted) values of y given specified values of x, and specified values for the interaction term.
I am not sure how to do that with Mplus. It sounds like you want to compute predicted y-values given your equation with interactions. If so, that can be done using methods developed for regular regression models, perhaps using a spreadsheet.
Carolyn CL posted on Friday, September 05, 2014 - 12:37 pm
Thanks for this.
In the end, given that there were no sig. conditional indirect effects nor moderated mediated effects, we decided to simply estimate the interaction term.
However, I noticed that inclusion of the interaction term (m1Xm2_2) changes the direction of the m2_2 direct effect on y (without the interaction term B = -.09, ns; with the interaction term B = .19,ns).
1) Is this likely a result of adjusting for the interaction term, or should I be concerned about potential multicollinearity?
I also noticed that in fig. A (Model 1) in Preacher, Rucker & Hayes (2007) it appears as though the interaction term (xm) is allowed to correlate with both x and m, but the syntax for Model 1 in the appendix only specifies a correlation between xm and m.
(2) Should only a correlation between xm and m be specified when estimating an interaction term?
I ask in part because my coefficients (size) and their significance level change in somewhat meaningful ways depending on whether I specify a correlation between xm and m, or include an additional correlation between xm and x.
1a. The coefficient has a different interpretation after including the product, and thus a different value. Prior to adding the product, c is the effect of m2_2 holding constant m1 (and all other predictors). After adding the product, c is the effect of m2_2 where m1 = 0 (holding constant all other predictors).
1b, 2. The code is outdated. I would add the covariance. Otherwise you risk introducing misfit. xm and m will almost certainly be correlated, and fixing this parameter to 0 can induce bias.
Carolyn CL posted on Monday, September 08, 2014 - 7:20 am
1) To be clear, when you say 'I would add the covariance', you mean 'xm WITH m' and 'xm WITH x'?
2) Also, should I be concerned that when I run the model as a multiple linear regression (in SPSS) and include the interaction term (m1Xm2_2) I get a VIF > 5 for the m2_2 coefficient?
3) My understanding is that the traditional approach taken to deal with multicollinearity induced by interaction terms is to mean center variables before creating the product term, but that the MSEM approach does not require centering of variables. Is this correct?
2, 3. These sound more like regression-related questions than Mplus-specific issues. But in general, centering has no effect on estimates or tests of interaction effects. You might pursue this topic on the SEMNET listserv.
Yan Liu posted on Saturday, September 13, 2014 - 8:17 am
Dear Dr. Preacher,
I conducted a multilevel moderated mediational model. MODEL: %WITHIN% m y1 y2; y1 ON Sex m; y2 ON Sex m;
%BETWEEN% x m y1 y2; mom ON Sex w x (a1) xw (a2); y1 ON Sex x xw w m (b1); y2 ON Sex x xw w m (b2);
The model is terminated normally. However, my model fit is bad. Do you think it's because my model doesn't fit the data well or because of cluster size or other issues? Thanks a lot!
Model fit: Chi-Square Test of Model Fit Value 636.624 Degrees of Freedom 7 P-Value 0.0000
RMSEA Estimate 0.286
CFI 0.677 TLI -0.244
SRMR Value for Within 0.235 Value for Between 0.021