I am studying the association between product quality measured by expert intermediary (overallScore) and that measured by online user rating. In particular, I hypothesize that the aforementioned association is dependent on the longevity of product use. For instance, I would expect a positive correlation if the user rating were given right after the product purchase; and negative correlation if the user rating were given after some considerable use of the product. The longevity of use (moder) is captured at four levels (1 = < 1 month, 2 = 1-3 months, 3 = 3-6 months, and 4 = > 6 months). The descriptive statistics of the three variables is given below:
Code:
sum overallScore rating moder
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
overallScore | 11,716 71.03175 14.30822 4 100
rating | 11,716 2.804797 1.704218 1 5
moder | 11,716 2.992147 1.234491 1 4
Now, my dataset has the following structure:
– User rating is captured at the individual level for a given product identified with a name_id (the total number of products is 109). The minimum number of ratings per product is 3, and the maximum is 583.
– Expert intermediary overallScore is captured at the name_id level.
– And finally, each name_id is associated with a product category_id.
In the end of this post I provide an example of the structure of the data I am using.
As far as I understand, following such data structure each rating is nested within name_id and each name_id is nested within category_id. Therefore, to formally test my hypothesis on the moderating role of longevity of use, I use a linear hierarchical model using -mixed- command. While I have no issues running the following model:
Code:
mixed overallScore rating || category_id:
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -45318.885
Iteration 1: log likelihood = -45318.885
Computing standard errors:
Mixed-effects ML regression Number of obs = 11,716
Group variable: category_id Number of groups = 109
Obs per group:
min = 3
avg = 107.5
max = 583
Wald chi2(1) = 20.86
Log likelihood = -45318.885 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
overallScore | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
rating | .3020026 .0661245 4.57 0.000 .1724009 .4316043
_cons | 69.16763 .9746409 70.97 0.000 67.25737 71.07789
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
category_id: Identity |
var(_cons) | 94.82431 13.48987 71.75073 125.3179
-----------------------------+------------------------------------------------
var(Residual) | 129.4131 1.698858 126.1258 132.786
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 4949.73 Prob >= chibar2 = 0.0000
estat icc
Residual intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
category_id | .4228747 .0348833 .3563758 .4922911
------------------------------------------------------------------------------
Code:
mixed overallScore rating || name_id: || category_id: Performing EM optimization: Performing gradient-based optimization: Iteration 0: log likelihood = 105812.11 (not concave) Iteration 1: log likelihood = 272460.46 (not concave) Iteration 2: log likelihood = 281690.62 (not concave) Iteration 3: log likelihood = 285747.12 (not concave) Iteration 4: log likelihood = 286066.56 (not concave) Iteration 5: log likelihood = 286093.57 (not concave) Iteration 6: log likelihood = 286098.91 (not concave) Iteration 7: log likelihood = 286099.8 (not concave) Iteration 8: log likelihood = 286100 (not concave) Iteration 9: log likelihood = 286100.05 (not concave) Iteration 10: log likelihood = 286100.05 (not concave) Iteration 11: log likelihood = 286100.05 (not concave) Iteration 12: log likelihood = 286100.05 (not concave) Iteration 13: log likelihood = 286100.05 (not concave) Iteration 14: log likelihood = 286100.05 (not concave) Iteration 15: log likelihood = 286100.05 (not concave) Iteration 16: log likelihood = 286100.05 (not concave) Iteration 17: log likelihood = 286100.05 (not concave) --Break--
Array
Code:
* Example generated by -dataex-. To install: ssc install dataex clear input long(category_id name_id) byte(overallScore rating) float moder 1 2955 85 1 4 1 1015 89 1 4 1 1015 89 1 1 1 2085 80 3 4 1 1120 68 1 1 1 2085 80 1 4 1 2085 80 1 3 1 2085 80 1 4 1 2955 85 5 4 1 2085 80 1 4 1 2085 80 2 4 1 2085 80 1 4 1 2085 80 2 4 1 2085 80 2 4 1 2085 80 5 4 1 2085 80 1 4 1 2085 80 2 4 1 1013 80 3 4 1 1015 89 2 4 1 1015 89 1 3 1 1013 80 1 4 1 1015 89 5 2 1 1015 89 5 4 1 2085 80 1 4 1 1015 89 1 1 1 2955 85 5 4 1 1013 80 1 3 1 2085 80 2 4 1 1015 89 1 2 1 1120 68 1 4 1 1119 89 5 2 1 127 71 1 3 1 2085 80 1 4 1 2085 80 5 4 1 2085 80 4 4 1 1119 89 5 4 1 2085 80 1 4 1 2085 80 1 4 1 1015 89 3 3 1 1015 89 1 1 1 2085 80 1 2 1 2085 80 1 4 1 2085 80 4 4 1 2085 80 4 4 1 2085 80 1 4 1 1015 89 1 1 1 1015 89 1 4 1 2085 80 1 4 1 2085 80 3 4 1 2085 80 1 3 end label values category_id category_id label def category_id 1 "aa_batteries", modify label values name_id name_id label def name_id 127 "AmazonBasics Performance AA Alkaline battery", modify label def name_id 1013 "Duracell Coppertop Duralock AA Alkaline battery", modify label def name_id 1015 "Duracell Quantum AA Alkaline battery", modify label def name_id 1119 "Energizer Ultimate Lithium AA battery", modify label def name_id 1120 "Energizer ecoAdvanced AA Alkaline battery", modify label def name_id 2085 "Kirkland Signature (Costco) AA Alkaline battery", modify label def name_id 2955 "Rayovac Fusion Advanced AA Alkaline battery", modify
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