多数人会认为“you think”是个插入语。如果去掉插入语，则句子成了“Choose whatever best."宾语从句结构就不完整了。基于这种观点的人会认为“is”是必不可少的的。去掉插入语后为“Choose whatever is best". 宾语从句结构完整。

但也有观点认为，you think并不是插入语，而是宾语从句的主语和谓语，不可去掉，whatever中隐含的关系代词是think的宾语，best是宾语补足语。句子的结构是这样的：

Choose anything that you think best.这似乎也能讲得通。但相比之下，带is似乎读起来更通顺。Choose anything that you think is best.

尽管带is还是不带is，语法上都能讲的通，但我个人倾向于is应该有。去掉is读起来总感觉有些别扭。

关于think的用法有以下例句说明：

She thought (that) he was kind and generous.

She thought him kind and generous.

正确的句子：Choose whatever you think is best.

you think 为插入语。去掉之后：

Choose whatever is best.

= Choose anything that is best.

把you think 加进去后：

Choose anything that you think is best.

英语中，what 或whatever 可以身兼两职，相当于：the thing that; the things that, everything that, anything that。我们给它起个了名字：复合连接代词，复合关系代词，缩合连接代词，等。

同意cgh007老师解答，以上2种都正确

理解1：whatever you think 作宾语，后面BEST 作宾补理解

理解2：whatever作宾语，YOU THINK 作插入语，BEST 作宾补理解