but the feedback I received was quite adament that I was using the wrong model and insisted I used a mlm approach given the hierarchical nature of my data.
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Just to be clear, I suspect that the person who was so adamant does not fully understand these Stata commands. -xtreg, re- and -mixed- estimate the same model when you have only a two-level hierarchy, no random slopes, and independent covariance structure. -mixed- is more flexible in that you can have more levels, include random slopes, and a range of possible covariance structures. But for the simple case we are discussing here: two levels, no random slopes, independent covariance, they are exactly the same model. The method of estimating the parameters of the model differs, but when both of them succeeds, the results will be essentially identical. -
That is interesting, I must say I was not aware of that myself either, so thanks for the clarification. Given that knowledge I am leaning toward choosing to run my random effects model as I know that works and if I understand correctly will yield the same results.Originally posted by Clyde Schechter View Post
With regard to the slopes and independent covariance I must say I am not entirely sure if I need random slopes or whether I can assume independent covariances. In my original model I applied a fixed effects xtregar regression as my models were dealing with autocorrelation. Now I am thinking about the data I have, I am actually more confident in saying a random effects model would be better suited. What would your opinion be on letting go of mlm given all this?Comment
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I looked into this and found that it still will not converge, results below;Originally posted by Daniel Schaefer View Post
I have a question that might clear up some of your concerns regarding my panel data. Previously I set my panel data using:Code:do "C:\Users\jesse\AppData\Local\Temp\STD2efc_000000.tmp" . //adjusted tolerance . mixed ln_Revenue c.CharismaticValuebased##i.crisis i.crisis HHI Political GDPG Inflation ln_GDP ln_Assets || Country:, iterate(10) tolerance(1e-5) Performing EM optimization ... Performing gradient-based optimization: Iteration 0: Log likelihood = -687343.55 Iteration 1: Log likelihood = -687343.55 (backed up) Iteration 2: Log likelihood = -687343.55 (backed up) Iteration 3: Log likelihood = -687343.55 (backed up) Iteration 4: Log likelihood = -687343.55 (backed up) Iteration 5: Log likelihood = -687343.55 (backed up) Iteration 6: Log likelihood = -687343.55 (backed up) Iteration 7: Log likelihood = -687343.55 (backed up) Iteration 8: Log likelihood = -687343.55 (backed up) Iteration 9: Log likelihood = -687343.55 (backed up) Iteration 10: Log likelihood = -687343.55 (backed up) convergence not achieved Computing standard errors ... Mixed-effects ML regression Number of obs = 354,283 Group variable: Country Number of groups = 25 Obs per group: min = 852 avg = 14,171.3 max = 65,676 Wald chi2(9) = 216935.24 Log likelihood = -687343.55 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------------------------ ln_Revenue | Coefficient Std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | .64255 .3643443 1.76 0.078 -.0715518 1.356652 1.crisis | -.2174034 .1057229 -2.06 0.040 -.4246164 -.0101905 | crisis#c.CharismaticValuebased | 1 | -.03602 .0183068 -1.97 0.049 -.0719005 -.0001394 | HHI | .0001683 .0000567 2.97 0.003 .000057 .0002795 Political | -.1756487 .0253797 -6.92 0.000 -.2253919 -.1259055 GDPG | .0232012 .0007719 30.06 0.000 .0216882 .0247142 Inflation | .0279139 .0014549 19.19 0.000 .0250623 .0307654 ln_GDP | .4946042 .0404051 12.24 0.000 .4154117 .5737967 ln_Assets | .6557599 .0014367 456.43 0.000 .652944 .6585758 _cons | -13.07199 2.437147 -5.36 0.000 -17.84871 -8.295271 ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ Country: Identity | var(_cons) | .355698 .1054047 .1989955 .6357988 -----------------------------+------------------------------------------------ var(Residual) | 2.834431 .0067348 2.821262 2.847662 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 12861.66 Prob >= chibar2 = 0.0000 Warning: Convergence not achieved. . mixed ln_Revenue c.CharismaticValuebased##i.crisis i.crisis HHI Political GDPG Inflation ln_GDP ln_Assets || Country:, iterate(10) tolerance(1e-6) Performing EM optimization ... Performing gradient-based optimization: Iteration 0: Log likelihood = -687343.55 Iteration 1: Log likelihood = -687343.55 (backed up) Iteration 2: Log likelihood = -687343.55 (backed up) Iteration 3: Log likelihood = -687343.55 (backed up) Iteration 4: Log likelihood = -687343.55 (backed up) Iteration 5: Log likelihood = -687343.55 (backed up) Iteration 6: Log likelihood = -687343.55 (backed up) Iteration 7: Log likelihood = -687343.55 (backed up) Iteration 8: Log likelihood = -687343.55 (backed up) Iteration 9: Log likelihood = -687343.55 (backed up) Iteration 10: Log likelihood = -687343.55 (backed up) convergence not achieved Computing standard errors ... Mixed-effects ML regression Number of obs = 354,283 Group variable: Country Number of groups = 25 Obs per group: min = 852 avg = 14,171.3 max = 65,676 Wald chi2(9) = 216935.24 Log likelihood = -687343.55 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------------------------ ln_Revenue | Coefficient Std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | .64255 .3643443 1.76 0.078 -.0715518 1.356652 1.crisis | -.2174034 .1057229 -2.06 0.040 -.4246164 -.0101905 | crisis#c.CharismaticValuebased | 1 | -.03602 .0183068 -1.97 0.049 -.0719005 -.0001394 | HHI | .0001683 .0000567 2.97 0.003 .000057 .0002795 Political | -.1756487 .0253797 -6.92 0.000 -.2253919 -.1259055 GDPG | .0232012 .0007719 30.06 0.000 .0216882 .0247142 Inflation | .0279139 .0014549 19.19 0.000 .0250623 .0307654 ln_GDP | .4946042 .0404051 12.24 0.000 .4154117 .5737967 ln_Assets | .6557599 .0014367 456.43 0.000 .652944 .6585758 _cons | -13.07199 2.437147 -5.36 0.000 -17.84871 -8.295271 ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ Country: Identity | var(_cons) | .355698 .1054047 .1989955 .6357988 -----------------------------+------------------------------------------------ var(Residual) | 2.834431 .0067348 2.821262 2.847662 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 12861.66 Prob >= chibar2 = 0.0000 Warning: Convergence not achieved. . mixed ln_Revenue c.CharismaticValuebased##i.crisis i.crisis HHI Political GDPG Inflation ln_GDP ln_Assets || Country:, iterate(10) tolerance(1e-7) Performing EM optimization ... Performing gradient-based optimization: Iteration 0: Log likelihood = -687343.55 Iteration 1: Log likelihood = -687343.55 (backed up) Iteration 2: Log likelihood = -687343.55 (backed up) Iteration 3: Log likelihood = -687343.55 (backed up) Iteration 4: Log likelihood = -687343.55 (backed up) Iteration 5: Log likelihood = -687343.55 (backed up) Iteration 6: Log likelihood = -687343.55 (backed up) Iteration 7: Log likelihood = -687343.55 (backed up) Iteration 8: Log likelihood = -687343.55 (backed up) Iteration 9: Log likelihood = -687343.55 (backed up) Iteration 10: Log likelihood = -687343.55 (backed up) convergence not achieved Computing standard errors ... Mixed-effects ML regression Number of obs = 354,283 Group variable: Country Number of groups = 25 Obs per group: min = 852 avg = 14,171.3 max = 65,676 Wald chi2(9) = 216935.24 Log likelihood = -687343.55 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------------------------ ln_Revenue | Coefficient Std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | .64255 .3643443 1.76 0.078 -.0715518 1.356652 1.crisis | -.2174034 .1057229 -2.06 0.040 -.4246164 -.0101905 | crisis#c.CharismaticValuebased | 1 | -.03602 .0183068 -1.97 0.049 -.0719005 -.0001394 | HHI | .0001683 .0000567 2.97 0.003 .000057 .0002795 Political | -.1756487 .0253797 -6.92 0.000 -.2253919 -.1259055 GDPG | .0232012 .0007719 30.06 0.000 .0216882 .0247142 Inflation | .0279139 .0014549 19.19 0.000 .0250623 .0307654 ln_GDP | .4946042 .0404051 12.24 0.000 .4154117 .5737967 ln_Assets | .6557599 .0014367 456.43 0.000 .652944 .6585758 _cons | -13.07199 2.437147 -5.36 0.000 -17.84871 -8.295271 ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ Country: Identity | var(_cons) | .355698 .1054047 .1989955 .6357988 -----------------------------+------------------------------------------------ var(Residual) | 2.834431 .0067348 2.821262 2.847662 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 12861.66 Prob >= chibar2 = 0.0000 Warning: Convergence not achieved. . mixed ln_Revenue c.CharismaticValuebased##i.crisis i.crisis HHI Political GDPG Inflation ln_GDP ln_Assets || Country:, iterate(10) tolerance(1e-8) Performing EM optimization ... Performing gradient-based optimization: Iteration 0: Log likelihood = -687343.55 Iteration 1: Log likelihood = -687343.55 (backed up) Iteration 2: Log likelihood = -687343.55 (backed up) Iteration 3: Log likelihood = -687343.55 (backed up) Iteration 4: Log likelihood = -687343.55 (backed up) Iteration 5: Log likelihood = -687343.55 (backed up) Iteration 6: Log likelihood = -687343.55 (backed up) Iteration 7: Log likelihood = -687343.55 (backed up) Iteration 8: Log likelihood = -687343.55 (backed up) Iteration 9: Log likelihood = -687343.55 (backed up) Iteration 10: Log likelihood = -687343.55 (backed up) convergence not achieved Computing standard errors ... Mixed-effects ML regression Number of obs = 354,283 Group variable: Country Number of groups = 25 Obs per group: min = 852 avg = 14,171.3 max = 65,676 Wald chi2(9) = 216935.24 Log likelihood = -687343.55 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------------------------ ln_Revenue | Coefficient Std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | .64255 .3643443 1.76 0.078 -.0715518 1.356652 1.crisis | -.2174034 .1057229 -2.06 0.040 -.4246164 -.0101905 | crisis#c.CharismaticValuebased | 1 | -.03602 .0183068 -1.97 0.049 -.0719005 -.0001394 | HHI | .0001683 .0000567 2.97 0.003 .000057 .0002795 Political | -.1756487 .0253797 -6.92 0.000 -.2253919 -.1259055 GDPG | .0232012 .0007719 30.06 0.000 .0216882 .0247142 Inflation | .0279139 .0014549 19.19 0.000 .0250623 .0307654 ln_GDP | .4946042 .0404051 12.24 0.000 .4154117 .5737967 ln_Assets | .6557599 .0014367 456.43 0.000 .652944 .6585758 _cons | -13.07199 2.437147 -5.36 0.000 -17.84871 -8.295271 ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ Country: Identity | var(_cons) | .355698 .1054047 .1989955 .6357988 -----------------------------+------------------------------------------------ var(Residual) | 2.834431 .0067348 2.821262 2.847662 ------------------------------------------------------------------------------ LR test vs. linear model: chibar2(01) = 12861.66 Prob >= chibar2 = 0.0000 Warning: Convergence not achieved. . end of do-file
I believe that is why it results in the high number of groups. Given my research on the effect of country-level leadership on firm-level Revenue and Current ratio, I had declared it with groups of individual firms per country. Now I am wondering whether this is in error, I tried respecifying my model using the advice of Clyde but incorporating my 'year' variable as I am interested in the changes over the years given my pre-crisis and crisis periods and want to compare them. I modified it like this;Code://setting panel data egen panel_id = group(Company Country) xtset panel_id year
but that results in new errors;Code:egen panel_id = group(Country) xtset panel_id year
I understand that this stems from the fact that I have multiple companies within the same year in the same country. I assume aggregation will solve this issue, but I am unsure whether this is a proper way to proceed given all my previous troubles.Code:. //setting panel data . egen panel_id = group(Country) . xtset panel_id year repeated time values within panel r(451); end of do-file r(451); . duplicates report Duplicates in terms of all variables -------------------------------------- Copies | Observations Surplus ----------+--------------------------- 1 | 433931 0 --------------------------------------Comment
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I can't really advise you on these questions. They are more substantive than statistical. Random slopes are a form of interaction: cross-level interactions. As with simpler models, the appropriateness of including interaction terms depends on whether the effects in the model are contingent on each other in the real world data generating process. Similarly, the need for estimating autocorrelation among error terms depends on whether the real world data generating process includes those. Often you can get guidance on these questions from previous studies of a similar design involving the same or similar variables and make this decision in advance of starting data analysis. If not, then the safest method is often to try things both ways and see which produces a better model (meaning one that fits the data better without overfitting the noise, not meaning one whose coefficients are more in line with your preferences). Sometimes you can make these decisions based just on study design and statistical considerations: a small data set cannot accommodate a large number of model degrees of freedom in the analysis. But the conclusion to draw from that might just be that the data set is inadequate for answering the study questions, not that a model omitting some important aspect of the data is OK.
I think these are questions you need to take up with people who have expertise in the field you are working in.Comment
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Thanks for your response Clyde, very much appreciated again. I decided to bring my DVs to the country-level as well to make it a country-level comparison between leadership styles and financial performance of the hotel industry in the respective county, no longer requiring a mlm approach in general and proceeding with xtregar re. Running my initial models shows promising results with high r-squared values so I will continue on this road.Originally posted by Clyde Schechter View Post
Best wishes for 2024!Comment
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I feel pretty stuck right now. My hausman test determined RE model is the way to go but it was indefinitive, I believe because it drops my time-consistent variable,
Code:. do "C:\Users\jesse\AppData\Local\Temp\STD4d48_000000.tmp" . xtreg ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG Inflation Political ln_Assets ln_GDP Charismatic > Controls, re Random-effects GLS regression Number of obs = 199 Group variable: Countryid Number of groups = 25 R-squared: Obs per group: Within = 0.9149 min = 7 Between = 0.9189 avg = 8.0 Overall = 0.9174 max = 8 Wald chi2(10) = 2032.94 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 ------------------------------------------------------------------------------------------------ ln_Revenue | Coefficient Std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 1.339 .3757337 3.56 0.000 .6025754 2.075424 | crisis#c.CharismaticValuebased | 1 | .0003871 .0757 0.01 0.996 -.1479821 .1487564 | 1.crisis | -.4071218 .4375816 -0.93 0.352 -1.264766 .4505223 HHI | 9.87e-06 .0000544 0.18 0.856 -.0000967 .0001165 GDPG | .0161741 .0035483 4.56 0.000 .0092195 .0231286 Inflation | .0364583 .005248 6.95 0.000 .0261724 .0467441 Political | -.0324715 .0790676 -0.41 0.681 -.187441 .1224981 ln_Assets | .7888723 .022642 34.84 0.000 .7444948 .8332498 ln_GDP | .1984057 .0619121 3.20 0.001 .0770602 .3197511 CharismaticControls | -.5356591 .1466865 -3.65 0.000 -.8231593 -.2481589 _cons | -10.79411 2.674701 -4.04 0.000 -16.03643 -5.55179 -------------------------------+---------------------------------------------------------------- sigma_u | .39528599 sigma_e | .15829904 rho | .86179118 (fraction of variance due to u_i) ------------------------------------------------------------------------------------------------ . est store random . xtreg ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG Inflation Political ln_Assets ln_GDP Charismatic > Controls, fe note: CharismaticValuebased omitted because of collinearity. note: CharismaticControls omitted because of collinearity. Fixed-effects (within) regression Number of obs = 199 Group variable: Countryid Number of groups = 25 R-squared: Obs per group: Within = 0.9155 min = 7 Between = 0.8417 avg = 8.0 Overall = 0.8482 max = 8 F(8, 166) = 224.82 corr(u_i, Xb) = -0.1485 Prob > F = 0.0000 ------------------------------------------------------------------------------------------------ ln_Revenue | Coefficient Std. err. t P>|t| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 0 (omitted) | crisis#c.CharismaticValuebased | 1 | .0043297 .0752718 0.06 0.954 -.1442837 .1529431 | 1.crisis | -.4305708 .4357462 -0.99 0.325 -1.29089 .4297481 HHI | .0000112 .0000565 0.20 0.843 -.0001004 .0001227 GDPG | .0158474 .0035799 4.43 0.000 .0087794 .0229154 Inflation | .0341004 .0057555 5.92 0.000 .0227371 .0454638 Political | -.1346436 .1003644 -1.34 0.182 -.3327988 .0635116 ln_Assets | .7837399 .0240839 32.54 0.000 .7361897 .8312902 ln_GDP | .2894671 .1671845 1.73 0.085 -.0406149 .6195491 CharismaticControls | 0 (omitted) _cons | -5.500988 4.447973 -1.24 0.218 -14.28288 3.280902 -------------------------------+---------------------------------------------------------------- sigma_u | .55697641 sigma_e | .15829904 rho | .92526101 (fraction of variance due to u_i) ------------------------------------------------------------------------------------------------ F test that all u_i=0: F(24, 166) = 56.30 Prob > F = 0.0000 . est store fixed . hausman fixed random Note: the rank of the differenced variance matrix (7) does not equal the number of coefficients being tested (8); be sure this is what you expect, or there may be problems computing the test. Examine the output of your estimators for anything unexpected and possibly consider scaling your variables so that the coefficients are on a similar scale. ---- Coefficients ---- | (b) (B) (b-B) sqrt(diag(V_b-V_B)) | fixed random Difference Std. err. -------------+---------------------------------------------------------------- crisis#| c. | Charismati~d | 1 | .0043297 .0003871 .0039426 . 1.crisis | -.4305708 -.4071218 -.023449 . HHI | .0000112 9.87e-06 1.33e-06 .0000153 GDPG | .0158474 .0161741 -.0003266 .0004746 Inflation | .0341004 .0364583 -.0023578 .0023631 Political | -.1346436 -.0324715 -.1021722 .0618169 ln_Assets | .7837399 .7888723 -.0051324 .0082082 ln_GDP | .2894671 .1984057 .0910615 .1552982 ------------------------------------------------------------------------------ b = Consistent under H0 and Ha; obtained from xtreg. B = Inconsistent under Ha, efficient under H0; obtained from xtreg. Test of H0: Difference in coefficients not systematic chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B) = 4.11 Prob > chi2 = 0.7670 (V_b-V_B is not positive definite) . end of do-file
The random effect model was supported by Breusch and Pagan Lagrangian multiplier test for random effects and heteroskedasticity providing strong evidence supporting the use of a random effects model with consideration for autocorrelation (xtregar re). The Wooldridge test result (Prob > F = 0.0110) indicates the presence of first-order autocorrelation in my panel data, which is effectively addressed by the xtregar model, but this model does not address heteroskedasticity The Breusch and Pagan test (chibar2(01) = 391.78, Prob > chibar2 = 0.0000) confirms the existence of significant random effects but also of heteroskedasticity which would lean me to apply xtreg, re vce(robust). I am aware that applying a fixed effects model could help mitigate against these issues but provided my theoretical framework, and the tests above, in combination with the model dropping my independent variable and one of my control variables wants me to stay clear of that option.
For what it is worth the fit of my models is as follows;
Xtreg, re vce(robust):
Xtregar, re:Code:. xtreg ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG Inflation Political ln_Assets ln_GDP Charismatic > Controls, re vce(robust) Random-effects GLS regression Number of obs = 199 Group variable: Countryid Number of groups = 25 R-squared: Obs per group: Within = 0.9149 min = 7 Between = 0.9189 avg = 8.0 Overall = 0.9174 max = 8 Wald chi2(10) = 4687.18 corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000 (Std. err. adjusted for 25 clusters in Countryid) ------------------------------------------------------------------------------------------------ | Robust ln_Revenue | Coefficient std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 1.339 .4171228 3.21 0.001 .5214543 2.156545 | crisis#c.CharismaticValuebased | 1 | .0003871 .1211898 0.00 0.997 -.2371405 .2379148 | 1.crisis | -.4071218 .6953072 -0.59 0.558 -1.769899 .9556554 HHI | 9.87e-06 .0000285 0.35 0.730 -.0000461 .0000658 GDPG | .0161741 .0049739 3.25 0.001 .0064254 .0259227 Inflation | .0364583 .0083884 4.35 0.000 .0200173 .0528992 Political | -.0324715 .0696303 -0.47 0.641 -.1689443 .1040013 ln_Assets | .7888723 .0234967 33.57 0.000 .7428196 .8349249 ln_GDP | .1984057 .0604838 3.28 0.001 .0798596 .3169517 CharismaticControls | -.5356591 .156792 -3.42 0.001 -.8429658 -.2283524 _cons | -10.79411 2.719071 -3.97 0.000 -16.12339 -5.464827 -------------------------------+---------------------------------------------------------------- sigma_u | .39528599 sigma_e | .15829904 rho | .86179118 (fraction of variance due to u_i) ------------------------------------------------------------------------------------------------
Code:. xtregar ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG Inflation Political ln_Assets ln_GDP Charismat > icControls, re RE GLS regression with AR(1) disturbances Number of obs = 199 Group variable: Countryid Number of groups = 25 R-squared: Obs per group: Within = 0.9130 min = 7 Between = 0.9236 avg = 8.0 Overall = 0.9214 max = 8 Wald chi2(11) = 1792.89 corr(u_i, Xb) = 0 (assumed) Prob > chi2 = 0.0000 ------------------- theta -------------------- min 5% median 95% max 0.7430 0.7571 0.7571 0.7571 0.7571 ------------------------------------------------------------------------------------------------ ln_Revenue | Coefficient Std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 1.263651 .3043116 4.15 0.000 .6672115 1.860091 | crisis#c.CharismaticValuebased | 1 | .001307 .0899475 0.01 0.988 -.1749867 .1776008 | 1.crisis | -.4140793 .5201949 -0.80 0.426 -1.433643 .6054839 HHI | .0000399 .0000539 0.74 0.458 -.0000656 .0001455 GDPG | .0129674 .0032996 3.93 0.000 .0065003 .0194346 Inflation | .0392117 .0052563 7.46 0.000 .0289096 .0495138 Political | .0389566 .075225 0.52 0.605 -.1084817 .1863948 ln_Assets | .7867611 .0254949 30.86 0.000 .7367921 .8367302 ln_GDP | .201084 .052698 3.82 0.000 .0977979 .3043702 CharismaticControls | -.4985161 .1195439 -4.17 0.000 -.7328179 -.2642143 _cons | -10.43879 2.176443 -4.80 0.000 -14.70454 -6.173043 -------------------------------+---------------------------------------------------------------- rho_ar | .29331591 (estimated autocorrelation coefficient) sigma_u | .32852848 sigma_e | .17272958 rho_fov | .78343419 (fraction of variance due to u_i) ------------------------------------------------------------------------------------------------ . end of do-file
Xtreg, fe vce(robust):
To answer my hypothesis, I only need to study the interaction term, but I am really trying my best to bring proper results to the table. I just cannot figure out a way to deal with all my problems. Is there anyone that could provide me with some advice, or relevant sources I can look into on how to proceed? It feels like I am stuck at a crossroads on how to proceed, but I have to choose between three options, and none of them seem to solve all the issues.Code:. xtreg ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG Inflation Political ln_Assets ln_GDP Charismatic > Controls, fe vce(robust) note: CharismaticValuebased omitted because of collinearity. note: CharismaticControls omitted because of collinearity. Fixed-effects (within) regression Number of obs = 199 Group variable: Countryid Number of groups = 25 R-squared: Obs per group: Within = 0.9155 min = 7 Between = 0.8417 avg = 8.0 Overall = 0.8482 max = 8 F(8, 24) = 380.51 corr(u_i, Xb) = -0.1485 Prob > F = 0.0000 (Std. err. adjusted for 25 clusters in Countryid) ------------------------------------------------------------------------------------------------ | Robust ln_Revenue | Coefficient std. err. t P>|t| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 0 (omitted) | crisis#c.CharismaticValuebased | 1 | .0043297 .1211158 0.04 0.972 -.2456411 .2543005 | 1.crisis | -.4305708 .6968927 -0.62 0.542 -1.868887 1.007745 HHI | .0000112 .0000314 0.36 0.725 -.0000537 .0000761 GDPG | .0158474 .0049517 3.20 0.004 .0056276 .0260673 Inflation | .0341004 .0099366 3.43 0.002 .0135924 .0546085 Political | -.1346436 .0950652 -1.42 0.170 -.3308486 .0615614 ln_Assets | .7837399 .0209232 37.46 0.000 .7405565 .8269233 ln_GDP | .2894671 .2180609 1.33 0.197 -.1605885 .7395227 CharismaticControls | 0 (omitted) _cons | -5.500988 5.835328 -0.94 0.355 -17.54451 6.542538 -------------------------------+---------------------------------------------------------------- sigma_u | .55697641 sigma_e | .15829904 rho | .92526101 (fraction of variance due to u_i) ------------------------------------------------------------------------------------------------Comment
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What about switching over to mixed, which allows for an autoregressive residual correlation structure and for different standard error types?
Code:mixed ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG /// Inflation Political ln_Assets ln_GDP Charismat icControls || Countryid: , /// residuals(ar 1, t(time_variable)) vce(robust)Comment
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Thank you so much Erik, you just made my day. I have been struggling running tests and trying alternative approaches for hours today and I just could not get it to work and solve my issues, and based on a fraction of the information I have available you just managed to get it to work. Again, thank you so much!Originally posted by Erik Ruzek View Post
Code:. mixed ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG /// > Inflation Political ln_Assets ln_GDP CharismaticControls || Countryid: , /// > residuals(ar 1, t(year)) vce(robust) Obtaining starting values by EM ... Performing gradient-based optimization: Iteration 0: Log pseudolikelihood = 39.646494 Iteration 1: Log pseudolikelihood = 39.646494 (not concave) Iteration 2: Log pseudolikelihood = 47.679019 Iteration 3: Log pseudolikelihood = 48.591585 Iteration 4: Log pseudolikelihood = 48.619727 Iteration 5: Log pseudolikelihood = 48.61981 Iteration 6: Log pseudolikelihood = 48.61981 Computing standard errors ... Mixed-effects regression Number of obs = 199 Group variable: Countryid Number of groups = 25 Obs per group: min = 7 avg = 8.0 max = 8 Wald chi2(10) = 5440.32 Log pseudolikelihood = 48.61981 Prob > chi2 = 0.0000 (Std. err. adjusted for 25 clusters in Countryid) ------------------------------------------------------------------------------------------------ | Robust ln_Revenue | Coefficient std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 1.26116 .3860361 3.27 0.001 .504543 2.017777 | crisis#c.CharismaticValuebased | 1 | .0049884 .129382 0.04 0.969 -.2485956 .2585724 | 1.crisis | -.4319053 .7433895 -0.58 0.561 -1.888922 1.025111 HHI | .000043 .0000272 1.58 0.114 -.0000103 .0000964 GDPG | .0120583 .004544 2.65 0.008 .0031523 .0209643 Inflation | .039591 .0071666 5.52 0.000 .0255447 .0536374 Political | .0349166 .0625835 0.56 0.577 -.0877448 .1575779 ln_Assets | .7891284 .0209617 37.65 0.000 .7480443 .8302124 ln_GDP | .202211 .0543793 3.72 0.000 .0956295 .3087925 CharismaticControls | -.4968404 .1406497 -3.53 0.000 -.7725088 -.221172 _cons | -10.48755 2.565812 -4.09 0.000 -15.51645 -5.458649 ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------ | Robust Random-effects parameters | Estimate std. err. [95% conf. interval] -----------------------------+------------------------------------------------ Countryid: Identity | var(_cons) | .129686 .03628 .0749492 .224398 -----------------------------+------------------------------------------------ Residual: AR(1) | rho | .4436219 .1180501 .1864588 .6438935 var(e) | .0305616 .0070029 .0195043 .0478875 ------------------------------------------------------------------------------ .
I will proceed running with mixed models for the remainder of my regressions!Comment
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Hmm, so I guess the mixed model would not converge earlier in the thread because it was underspecified without the residual structure. Neat.Comment
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I aggregated my hotel-level data to the country level to bring all variables to the country level and draw industry-wide conclusions rather than on the individual hotel level. Not sure if that could have affected the convergence now, or if it is the residual specifications. That is beyond my current capabilities sadly.Originally posted by Daniel Schaefer View PostComment
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Yeah, I remember mixed was used earlier and there were a lot more observations. What happened to all those? Nevermind, addressed in #25!
Also, is the c.CharismaticValuebased#i.crisis interaction cross-level, meaning that one of the variables is at the observation level and the other is at the country level? If so, then you should specify it as having a random (varying) slope. See Hesig & Schafer (2019).
Code:mixed ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG /// Inflation Political ln_Assets ln_GDP Charismat icControls || Countryid: crisis , cov(un) /// residuals(ar 1, t(time_variable)) vce(robust)Comment
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Crisis is binary indicating crisis or non crisis for the years included in my dataset;Originally posted by Erik Ruzek View Post
So I assume at the observation level?Code:gen crisis = year >= 2020
Edit: I will look into the paper, I am still very confused as to how the slopes work, so that will definitely contribute to my understanding.Comment
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An observation variable (not a technical term) varies within clusters. A cluster variable is constant within clusters but varies between clusters. So when you interact a variable that varies within clusters with a variable that varies between clusters, it is called a cross-level interaction. The Hesig & Schaffer paper addresses this situation.
For variables that vary within clusters, you can specify the model to have non-varying (often called "fixed") or varying (often called "random") slopes. If you opt for a varying/random slope, then you are allowing the association between that variable and the outcome to vary by cluster. This induces an additional variance term for the slope in the random-effects part of the model. The additional syntax of cov(un) allows for the slope and intercept to covary, which is often a good idea and typically provides better model fit than a model that excludes it.
You will see that when allowing a variable to have a random or varying slope, you continue to get a slope estimate in the top set of parameter estimates. This is the mean slope for the population around which all the country slopes vary.Comment
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Interesting. I went through the article, and if I understand correctly, the inclusion of random slopes is done to capture unexplained contextual variation in relationships between variables? Or as you explained it, the variables are allowed to vary by country?Originally posted by Erik Ruzek View Post
I am wondering though, the authors propose that you should always include random slopes for the lower-level variables involved in cross-level interactions in mixed-effects models, but the inclusion of the varying slopes makes my AIC & BIC values less negative.
I ran the following models, with model 1 being random slopes and model 2 not specifying random slopes ;
The model with the random slopes has:Code:. mixed ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG /// > Inflation Political ln_Assets ln_GDP CharismaticControls || Countryid: crisis , cov(un) /// > residuals(ar 1, t(year)) vce(robust) Obtaining starting values by EM ... Performing gradient-based optimization: Iteration 0: Log pseudolikelihood = 46.857674 Iteration 1: Log pseudolikelihood = 49.990457 Iteration 2: Log pseudolikelihood = 50.852714 Iteration 3: Log pseudolikelihood = 50.896779 Iteration 4: Log pseudolikelihood = 50.897016 Iteration 5: Log pseudolikelihood = 50.897016 Computing standard errors ... Mixed-effects regression Number of obs = 199 Group variable: Countryid Number of groups = 25 Obs per group: min = 7 avg = 8.0 max = 8 Wald chi2(10) = 4662.01 Log pseudolikelihood = 50.897016 Prob > chi2 = 0.0000 (Std. err. adjusted for 25 clusters in Countryid) ------------------------------------------------------------------------------------------------ | Robust ln_Revenue | Coefficient std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 1.183889 .3800979 3.11 0.002 .4389104 1.928867 | crisis#c.CharismaticValuebased | 1 | .0066603 .1294148 0.05 0.959 -.246988 .2603086 | 1.crisis | -.4462518 .7429435 -0.60 0.548 -1.902394 1.009891 HHI | .0000466 .0000266 1.75 0.080 -5.60e-06 .0000987 GDPG | .0114903 .0046471 2.47 0.013 .0023821 .0205985 Inflation | .0398219 .0073862 5.39 0.000 .0253452 .0542985 Political | .0491699 .0664332 0.74 0.459 -.0810368 .1793766 ln_Assets | .7857556 .0175209 44.85 0.000 .7514152 .8200959 ln_GDP | .2019008 .0527926 3.82 0.000 .0984292 .3053723 CharismaticControls | -.4559882 .1360658 -3.35 0.001 -.7226722 -.1893042 _cons | -9.99609 2.561318 -3.90 0.000 -15.01618 -4.976 ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------ | Robust Random-effects parameters | Estimate std. err. [95% conf. interval] -----------------------------+------------------------------------------------ Countryid: Unstructured | var(crisis) | .0132031 .0099943 .0029947 .0582109 var(_cons) | .120477 .0357572 .0673395 .2155452 cov(crisis,_cons) | .0103949 .0105639 -.0103099 .0310996 -----------------------------+------------------------------------------------ Residual: AR(1) | rho | .4009766 .1534143 .0664203 .6544858 var(e) | .0263192 .0078923 .0146226 .0473721 ------------------------------------------------------------------------------ . est store CharRev . estat ic Akaike's information criterion and Bayesian information criterion ----------------------------------------------------------------------------- Model | N ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- CharRev | 199 . 50.89702 16 -69.79403 -17.10116 ----------------------------------------------------------------------------- Note: BIC uses N = number of observations. See [R] IC note. . //charismatic revenue . mixed ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG /// > Inflation Political ln_Assets ln_GDP CharismaticControls || Countryid: , /// > residuals(ar 1, t(year)) vce(robust) Obtaining starting values by EM ... Performing gradient-based optimization: Iteration 0: Log pseudolikelihood = 39.646494 Iteration 1: Log pseudolikelihood = 39.646494 (not concave) Iteration 2: Log pseudolikelihood = 47.679019 Iteration 3: Log pseudolikelihood = 48.591585 Iteration 4: Log pseudolikelihood = 48.619727 Iteration 5: Log pseudolikelihood = 48.61981 Iteration 6: Log pseudolikelihood = 48.61981 Computing standard errors ... Mixed-effects regression Number of obs = 199 Group variable: Countryid Number of groups = 25 Obs per group: min = 7 avg = 8.0 max = 8 Wald chi2(10) = 5440.32 Log pseudolikelihood = 48.61981 Prob > chi2 = 0.0000 (Std. err. adjusted for 25 clusters in Countryid) ------------------------------------------------------------------------------------------------ | Robust ln_Revenue | Coefficient std. err. z P>|z| [95% conf. interval] -------------------------------+---------------------------------------------------------------- CharismaticValuebased | 1.26116 .3860361 3.27 0.001 .504543 2.017777 | crisis#c.CharismaticValuebased | 1 | .0049884 .129382 0.04 0.969 -.2485956 .2585724 | 1.crisis | -.4319053 .7433895 -0.58 0.561 -1.888922 1.025111 HHI | .000043 .0000272 1.58 0.114 -.0000103 .0000964 GDPG | .0120583 .004544 2.65 0.008 .0031523 .0209643 Inflation | .039591 .0071666 5.52 0.000 .0255447 .0536374 Political | .0349166 .0625835 0.56 0.577 -.0877448 .1575779 ln_Assets | .7891284 .0209617 37.65 0.000 .7480443 .8302124 ln_GDP | .202211 .0543793 3.72 0.000 .0956295 .3087925 CharismaticControls | -.4968404 .1406497 -3.53 0.000 -.7725088 -.221172 _cons | -10.48755 2.565812 -4.09 0.000 -15.51645 -5.458649 ------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------ | Robust Random-effects parameters | Estimate std. err. [95% conf. interval] -----------------------------+------------------------------------------------ Countryid: Identity | var(_cons) | .129686 .03628 .0749492 .224398 -----------------------------+------------------------------------------------ Residual: AR(1) | rho | .4436219 .1180501 .1864588 .6438935 var(e) | .0305616 .0070029 .0195043 .0478875 ------------------------------------------------------------------------------ . est store CharRev . estat ic Akaike's information criterion and Bayesian information criterion ----------------------------------------------------------------------------- Model | N ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- CharRev | 199 . 48.61981 14 -69.23962 -23.13335 ----------------------------------------------------------------------------- Note: BIC uses N = number of observations. See [R] IC note.- higher log pseudolikelihood (50.897 vs 48.620)
- lower wald chi2 value (4662.01 vs 5440.32)
- more negative AIC (-69.794 vs -69.240)
- less negative BIC (-17.101 vs -23.133).
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I agree. With AIC and BIC, lower numbers are better. In addition to comparing IC, you can run a likelihood ratio test (lrtest in Stata) that compares the two log likelihoods given that the models are nested. By nested I mean that one can get from the random slope model to the random intercept model by constraining the random slope variance and random slope-intercept covariance to 0. This gives you two additional degrees of freedom. The likelihood ratio test follows a chi-square distribution except that the null hypothesis is on the boundary of the parameter space since variances from these models are > 0. Accordingly, you divide the p-value reported by lrtest by 2.
Code:mixed ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG /// Inflation Political ln_Assets ln_GDP Charismat icControls || Countryid: crisis , cov(un) /// residuals(ar 1, t(time_variable)) vce(robust) eststo ri mixed ln_Revenue CharismaticValuebased c.CharismaticValuebased#i.crisis i.crisis HHI GDPG /// Inflation Political ln_Assets ln_GDP Charismat icControls || Countryid: crisis , cov(un) /// residuals(ar 1, t(time_variable)) vce(robust) eststo rc lrtest rc ri, statsComment
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